Question 1

I walk six miles in a straight line in a direction north of east, and I end up four miles north and several miles east. How many degrees north of east have I walked?
A) 19$\degree$
B) 42$\degree$
C) 60$\degree$
D) 71$\degree$

Accepted Answer

The answer of I walk six miles in a straight...

Question 2

Find the sum of the following two vectors: (i) 50 units due east and (ii) 100 units 30$\degree$ south of west.
A) 100 units 30$\degree$south of west
B) 62 units 54$\degree$ south of west
C) 87 units 60$\degree$south of west
D) 62 units 15$\degree$ south of west

Accepted Answer

The correct answer is B because the sum of the two vectors is the vector that has a magnitude of 100 units and a direction of 30 degrees south of west.

Question 3

Arvin the Ant travels 30 cm eastward, then 25 cm northward, and finally 10 cm westward. In what direction is Arvin now in with respect to his starting point?
A) 59$\degree$N of E
B) 29$\degree$N of E
C) 29$\degree$N of W
D) 51$\degree$ N of E

Accepted Answer

The answer of Arvin the Ant travels 30 cm eastward,...

Question 4

A taxicab moves five blocks due north, five blocks due east, and another three blocks due north. Assume all blocks are of equal size. How far is the taxi from its starting point?
A) 13 blocks
B) 9.4 blocks
C) 9.2 blocks
D) 8.6 blocks

Accepted Answer

The taxi's total movement north is 8 blocks (5 + 3) and east is 5 blocks. Using the Pythagorean theorem (since the path forms a right triangle), the distance from the starting point is √(8^2 + 5^2) = √(64 + 25) = √89 ≈ 9.4 blocks.

Question 5

Vector  points north and vector  points east. If  , then vector  points:
A) north of east.
B) south of east.
C) north of west.
D) south of west.

Accepted Answer

The answer of Vector  points north and vector ...

Question 6

When three vectors are added graphically and form a closed triangle, the largest enclosed angle between any two of the vectors cannot be greater than:
A) 60$\degree$
B) 90$\degree$.
C) 180$\degree$.
D) No maximum exists.

Accepted Answer

The answer of When three vectors are added graphically and...

Question 7

In a 2-dimensional Cartesian coordinate system the x component of a given vector is equal to that vector's magnitude multiplied by which trigonometric function, with respect to the angle between vector and y axis?
A) sine
B) cosine
C) tangent
D) cotangent

Accepted Answer

The answer of In a 2-dimensional Cartesian coordinate system the...

Question 8

In a 2-dimensional Cartesian system, the y component of a vector is known, and the angle between vector and x axis is known. Which operation is used to calculate the magnitude of the vector (taken with respect to the y component)?
A) dividing by cosine
B) dividing by sine
C) multiplying by cosine
D) multiplying by sine

Accepted Answer

To find the magnitude of the vector using the y component and the angle with the x-axis, divide the y component by the sine of the angle.

Question 9

Vector  is 3.0 units in length and points along the positive x axis; vector  is 5.0 units in length and points along a direction 150$\degree$from the positive x axis. What is the magnitude of the resulting vector when vectors  and  are added?
A) 7.0
B) 6.7
C) 2.8
D) 2.1

Accepted Answer

The answer of Vector  is 3.0 units in length...

Question 10

A student adds two vectors with magnitudes of 200 and 70. Which one of the following is the only possible choice for the magnitude of their sum?
A) 100
B) 280
C) 200
D) 70

Accepted Answer

The answer of A student adds two vectors with magnitudes...

Question 11

Vector  is 5 m long and vector  is 12 m long. The length of the sum of the vectors must be:
A) some value from 7 m to 17 m.
B) 13 m.
C) 17 m.
D) 8 m.

Accepted Answer

The answer of Vector  is 5 m long and...

Question 12

In a 2-dimensional Cartesian coordinate system the y component of a given vector is equal to that vector's magnitude multiplied by which trigonometric function, with respect to the angle between vector and x axis?
A) sine
B) cosine
C) tangent
D) cotangent

Accepted Answer

The y component of a vector is equal to the vector's magnitude multiplied by the sine of the angle between the vector and the x-axis.

Question 13

Vector  is 3.0 units in length and points along the positive x axis; vector  is 5.0 units in length and points along a direction 150$\degree$from the positive x axis. What is the direction of their sum with respect to the positive x axis?
A) 62$\degree$
B) 13$\degree$
C) 118$\degree$
D) 103$\degree$

Accepted Answer

The answer of Vector  is 3.0 units in length...

Quiz 1: Introduction

I walk six miles in a straight line in a direction north of east, and I end up four miles north and several miles east. How many degrees north of east have I walked?

Find the sum of the following two vectors: (i) 50 units due east and (ii) 100 units 30 $\degree$ south of west.

Arvin the Ant travels 30 cm eastward, then 25 cm northward, and finally 10 cm westward. In what direction is Arvin now in with respect to his starting point?

A taxicab moves five blocks due north, five blocks due east, and another three blocks due north. Assume all blocks are of equal size. How far is the taxi from its starting point?

Vector points north and vector points east. If , then vector points:

When three vectors are added graphically and form a closed triangle, the largest enclosed angle between any two of the vectors cannot be greater than:

In a 2-dimensional Cartesian coordinate system the x component of a given vector is equal to that vector's magnitude multiplied by which trigonometric function, with respect to the angle between vector and y axis?

In a 2-dimensional Cartesian system, the y component of a vector is known, and the angle between vector and x axis is known. Which operation is used to calculate the magnitude of the vector (taken with respect to the y component) ?

A student adds two vectors with magnitudes of 200 and 70. Which one of the following is the only possible choice for the magnitude of their sum?

Vector is 5 m long and vector is 12 m long. The length of the sum of the vectors must be:

In a 2-dimensional Cartesian coordinate system the y component of a given vector is equal to that vector's magnitude multiplied by which trigonometric function, with respect to the angle between vector and x axis?