Question 1

Is the distance between a satellite and the earth a vector or a scalar?

Accepted Answer

scalar

Question 2

Which of the following would be described by vectors rather than scalars?

Accepted Answer

C, D

Question 3

A kite on a 26 meter string is flying with an angle of $33^{\circ}$ with the ground. What is the magnitude and the direction of the vector from the kite to the ground. Round numbers to 3 decimal places if necessary.

Accepted Answer

The vector points directly downward and has magnitude 14.161 meters

Question 4

Simplify $2(4 \vec{v}+6 \vec{w})+\vec{v}$

Accepted Answer

The answer of Simplify $2(4 \vec{v}+6 \vec{w})+\vec{v}$...

Question 5

Simplify $12 \vec{v}-3(4 \vec{v})$

Accepted Answer

The answer of Simplify $12 \vec{v}-3(4 \vec{v})$...

Question 6

Suppose a man starts at work and drives $8 \mathrm{~km}$ due south, and then drives $13 \mathrm{~km}$ southeast. How far is the man from work? Round numbers to 3 decimal places if necessary.

Accepted Answer

The answer of Suppose a man starts at work and...

Question 7

A canoe can travel $16 \mathrm{ft} \mathrm{sec}$ in still water. Suppose a river is flowing at a rate of 5 $\mathrm{ft} \mathrm{sec}$. If the canoe is traveling downstream at an angle of $45^{\circ}$ with the current, what is the speed of the canoe? Round numbers to 3 decimal places if necessary.

Accepted Answer

The answer of A canoe can travel $16 \mathrm{ft} \mathrm{sec}$...

Question 8

A man leaves his car and walks 2 miles northeast, 4 miles east, and then 8 miles southwest. How far is the person from his car? In what direction must he walk to head directly to his car? Round numbers to 3 decimal places if necessary.

Accepted Answer

The answer of A man leaves his car and walks...

Question 9

A man is sitting 9 meters above the ground in a tree which is 10 meters directly south of the fence corner of a field. A bird is spotted 2 meters above the ground and 8 meters directly north of the fence corner. How far is the man from the bird? Round your answer to 3 decimal places.

Accepted Answer

The answer of A man is sitting 9 meters above...

Question 10

A man is sitting 8 meters above the ground in a tree which is 10 meters directly south of the fence corner of a field. A bird is spotted 3 meters above the ground and 9 meters directly north of the fence corner. In what direction must the man face to look directly at the bird? Round your answer to 3 decimal places.

Accepted Answer

The answer of A man is sitting 8 meters above...

Question 11

A horse runs at a constant speed of $18 \mathrm{~m} \mathrm{sec}$. He starts at a fence and his path makes an angle of $13^{\circ}$ with the fence. After 9 seconds, how far is he from the fence? Round numbers to 3 decimal places if necessary.

Accepted Answer

The answer of A horse runs at a constant speed...

Question 12

What properties of vector addition and scalar multiplication are necessary to show $(5+a)(\vec{v}+\vec{w})=5 \vec{w}+a \vec{w}+5 \vec{v}+a \vec{v}$

Accepted Answer

The answer of What properties of vector addition and scalar...

Question 13

Does $-3 \vec{v}+5 \vec{v}$ point in the same direction as $\vec{v}$, the opposite direction, or neither?

Accepted Answer

The answer of Does $-3 \vec{v}+5 \vec{v}$ point in the...

Question 14

Let $\vec{v}$ be a vector of length 3 pointing $30^{\circ}$ north of east. Find the length and direction of $23 \vec{v}$.

Accepted Answer

The answer of Let $\vec{v}$ be a vector of length...

Question 15

Let $\vec{v}$ be a vector of length 3 pointing $30^{\circ}$ north of east. Find the length and direction of $-4 \vec{v}$.

Accepted Answer

The answer of Let $\vec{v}$ be a vector of length...

Question 16

Jack and Jill begin walking away from a water well. Jill walks 2 meters north, and then 12 meters east. When Jill stops, Jack is twice as far from the well as she is. How far is Jack from the well? Round numbers to 3 decimal places if necessary.

Accepted Answer

The answer of Jack and Jill begin walking away from...

Question 17

Jack and Jill begin walking away from a water well. Jill walks 3 meters north, and then 14 meters northeast. When Jill stops, Jack is half as far from the well as she is. How far is Jack from the well? Round numbers to 3 decimal places if necessary.

Accepted Answer

The answer of Jack and Jill begin walking away from...

Question 18

Jack and Jill begin walking away from a water well. Jill walks 4 meters west, and then 2 meters north. When Jill stops, Jack is three times as far from the well as she is, but in the opposite direction. If $\vec{v}$ is the vector pointing from Jack to the well, find the length and direction of $\vec{v}$. Round numbers to 3 decimal places if necessary.

Accepted Answer

The answer of Jack and Jill begin walking away from...

Question 19

Simplify the following: $3(2 \vec{v}+7 \vec{w})-(-3 \vec{v}-7 \vec{w})$

Accepted Answer

The answer of Simplify the following: \(3(2 \vec{v}+7 \vec{w})-(-3 \vec{v}-7...

Question 20

Simplify the following: $2(6 \vec{v}-\vec{w}-\vec{p})+9(\vec{v}-4 \vec{w}+\vec{p})$

Accepted Answer

The answer of Simplify the following: $2(6 \vec{v}-\vec{w}-\vec{p})+9(\vec{v}-4 \vec{w}+\vec{p})$...

Quiz 12: Vectors and Matrices

Is the distance between a satellite and the earth a vector or a scalar?

Which of the following would be described by vectors rather than scalars?

A kite on a 26 meter string is flying with an angle of $33^{\circ}$ with the ground. What is the magnitude and the direction of the vector from the kite to the ground. Round numbers to 3 decimal places if necessary.

Simplify $2(4 \vec{v}+6 \vec{w})+\vec{v}$

Simplify $12 \vec{v}-3(4 \vec{v})$

Suppose a man starts at work and drives $8 \mathrm{~km}$ due south, and then drives $13 \mathrm{~km}$ southeast. How far is the man from work? Round numbers to 3 decimal places if necessary.

A canoe can travel $16 \mathrm{ft} \mathrm{sec}$ in still water. Suppose a river is flowing at a rate of 5 $\mathrm{ft} \mathrm{sec}$ . If the canoe is traveling downstream at an angle of $45^{\circ}$ with the current, what is the speed of the canoe? Round numbers to 3 decimal places if necessary.

A man leaves his car and walks 2 miles northeast, 4 miles east, and then 8 miles southwest. How far is the person from his car? In what direction must he walk to head directly to his car? Round numbers to 3 decimal places if necessary.

A man is sitting 9 meters above the ground in a tree which is 10 meters directly south of the fence corner of a field. A bird is spotted 2 meters above the ground and 8 meters directly north of the fence corner. How far is the man from the bird? Round your answer to 3 decimal places.

A horse runs at a constant speed of $18 \mathrm{~m} \mathrm{sec}$ . He starts at a fence and his path makes an angle of $13^{\circ}$ with the fence. After 9 seconds, how far is he from the fence? Round numbers to 3 decimal places if necessary.

What properties of vector addition and scalar multiplication are necessary to show $(5+a)(\vec{v}+\vec{w})=5 \vec{w}+a \vec{w}+5 \vec{v}+a \vec{v}$

Does $-3 \vec{v}+5 \vec{v}$ point in the same direction as $\vec{v}$ , the opposite direction, or neither?

Let $\vec{v}$ be a vector of length 3 pointing $30^{\circ}$ north of east. Find the length and direction of $23 \vec{v}$ .

Let $\vec{v}$ be a vector of length 3 pointing $30^{\circ}$ north of east. Find the length and direction of $-4 \vec{v}$ .

Jack and Jill begin walking away from a water well. Jill walks 2 meters north, and then 12 meters east. When Jill stops, Jack is twice as far from the well as she is. How far is Jack from the well? Round numbers to 3 decimal places if necessary.

Jack and Jill begin walking away from a water well. Jill walks 3 meters north, and then 14 meters northeast. When Jill stops, Jack is half as far from the well as she is. How far is Jack from the well? Round numbers to 3 decimal places if necessary.

Simplify the following: $3(2 \vec{v}+7 \vec{w})-(-3 \vec{v}-7 \vec{w})$

Simplify the following: $2(6 \vec{v}-\vec{w}-\vec{p})+9(\vec{v}-4 \vec{w}+\vec{p})$

Quiz 12: Vectors and Matrices

Is the distance between a satellite and the earth a vector or a scalar?

Which of the following would be described by vectors rather than scalars?

A kite on a 26 meter string is flying with an angle of 33∘33^{\circ}33∘ with the ground. What is the magnitude and the direction of the vector from the kite to the ground. Round numbers to 3 decimal places if necessary.

Simplify 2(4v⃗+6w⃗)+v⃗2(4 \vec{v}+6 \vec{w})+\vec{v}2(4v+6w)+v

Simplify 12v⃗−3(4v⃗)12 \vec{v}-3(4 \vec{v})12v−3(4v)

Suppose a man starts at work and drives 8 km8 \mathrm{~km}8 km due south, and then drives 13 km13 \mathrm{~km}13 km southeast. How far is the man from work? Round numbers to 3 decimal places if necessary.

A man leaves his car and walks 2 miles northeast, 4 miles east, and then 8 miles southwest. How far is the person from his car? In what direction must he walk to head directly to his car? Round numbers to 3 decimal places if necessary.

A man is sitting 9 meters above the ground in a tree which is 10 meters directly south of the fence corner of a field. A bird is spotted 2 meters above the ground and 8 meters directly north of the fence corner. How far is the man from the bird? Round your answer to 3 decimal places.

A horse runs at a constant speed of 18 msec18 \mathrm{~m} \mathrm{sec}18 msec . He starts at a fence and his path makes an angle of 13∘13^{\circ}13∘ with the fence. After 9 seconds, how far is he from the fence? Round numbers to 3 decimal places if necessary.

What properties of vector addition and scalar multiplication are necessary to show (5+a)(v⃗+w⃗)=5w⃗+aw⃗+5v⃗+av⃗(5+a)(\vec{v}+\vec{w})=5 \vec{w}+a \vec{w}+5 \vec{v}+a \vec{v}(5+a)(v+w)=5w+aw+5v+av

Does −3v⃗+5v⃗-3 \vec{v}+5 \vec{v}−3v+5v point in the same direction as v⃗\vec{v}v , the opposite direction, or neither?

Let v⃗\vec{v}v be a vector of length 3 pointing 30∘30^{\circ}30∘ north of east. Find the length and direction of 23v⃗23 \vec{v}23v .

Let v⃗\vec{v}v be a vector of length 3 pointing 30∘30^{\circ}30∘ north of east. Find the length and direction of −4v⃗-4 \vec{v}−4v .

Jack and Jill begin walking away from a water well. Jill walks 2 meters north, and then 12 meters east. When Jill stops, Jack is twice as far from the well as she is. How far is Jack from the well? Round numbers to 3 decimal places if necessary.

Jack and Jill begin walking away from a water well. Jill walks 3 meters north, and then 14 meters northeast. When Jill stops, Jack is half as far from the well as she is. How far is Jack from the well? Round numbers to 3 decimal places if necessary.

Simplify the following: 3(2v⃗+7w⃗)−(−3v⃗−7w⃗)3(2 \vec{v}+7 \vec{w})-(-3 \vec{v}-7 \vec{w})3(2v+7w)−(−3v−7w)

Simplify the following: 2(6v⃗−w⃗−p⃗)+9(v⃗−4w⃗+p⃗)2(6 \vec{v}-\vec{w}-\vec{p})+9(\vec{v}-4 \vec{w}+\vec{p})2(6v−w−p​)+9(v−4w+p​)

A kite on a 26 meter string is flying with an angle of $33^{\circ}$ with the ground. What is the magnitude and the direction of the vector from the kite to the ground. Round numbers to 3 decimal places if necessary.

Simplify $2(4 \vec{v}+6 \vec{w})+\vec{v}$

Simplify $12 \vec{v}-3(4 \vec{v})$

Suppose a man starts at work and drives $8 \mathrm{~km}$ due south, and then drives $13 \mathrm{~km}$ southeast. How far is the man from work? Round numbers to 3 decimal places if necessary.

A horse runs at a constant speed of $18 \mathrm{~m} \mathrm{sec}$ . He starts at a fence and his path makes an angle of $13^{\circ}$ with the fence. After 9 seconds, how far is he from the fence? Round numbers to 3 decimal places if necessary.

What properties of vector addition and scalar multiplication are necessary to show $(5+a)(\vec{v}+\vec{w})=5 \vec{w}+a \vec{w}+5 \vec{v}+a \vec{v}$

Does $-3 \vec{v}+5 \vec{v}$ point in the same direction as $\vec{v}$ , the opposite direction, or neither?

Let $\vec{v}$ be a vector of length 3 pointing $30^{\circ}$ north of east. Find the length and direction of $23 \vec{v}$ .

Let $\vec{v}$ be a vector of length 3 pointing $30^{\circ}$ north of east. Find the length and direction of $-4 \vec{v}$ .

Simplify the following: $3(2 \vec{v}+7 \vec{w})-(-3 \vec{v}-7 \vec{w})$

Simplify the following: $2(6 \vec{v}-\vec{w}-\vec{p})+9(\vec{v}-4 \vec{w}+\vec{p})$