# Quiz 10: Vectors and the Geometry of Space

Mathematics

Free

Multiple Choice

C

Free

Multiple Choice

E

Free

Multiple Choice

B

Q 4Q 4

Find the velocity of a particle that has the given acceleration and the given initial velocity.
A)
B)
C)
D)
E)

Free

Multiple Choice

Free

Multiple Choice

Q 6Q 6

A force with magnitude N acts directly upward from the xy-plane on an object with mass kg. The object starts at the origin with initial velocity . Find its position function.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 7Q 7

A ball is thrown at an angle of to the ground. If the ball lands m away, what was the initial speed of the ball? Let .
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 8Q 8

Find the scalar tangential and normal components of acceleration of a particle with position vector
A)
B)
C)
D)

Free

Multiple Choice

Q 9Q 9

Find the velocity, acceleration, and speed of an object with position function for Sketch the path of the object and its velocity and acceleration vectors.

Free

Essay

Q 10Q 10

Find the velocity, acceleration, and speed of an object with position function for Sketch the path of the object and its velocity and acceleration vectors.

Free

Essay

Q 11Q 11

Find the velocity, acceleration, and speed of an object with position function for Sketch the path of the object and its velocity and acceleration vectors.

Free

Essay

Q 12Q 12

Find the velocity and position vectors of an object with acceleration initial velocity and initial position

Free

Essay

Q 13Q 13

A projectile is fired from ground level with an initial speed of 1100 ft/sec and an angle of elevation of
a. Find the range of the projectile.
b. What is the maximm height attained by the projectile?
c. What is the speed of the projectile at impact?
Round your answers to the nearest integer.

Free

Essay

Q 14Q 14

Find the scalar tangential and normal components of acceleration of a particle with position vector

Free

Essay

Free

Multiple Choice

Free

Multiple Choice

Q 17Q 17

Reparametrize the curve with respect to arc length measured from the point where in the direction of increasing .
A)
B)
C)
D)
E)

Free

Multiple Choice

Free

Multiple Choice

Q 19Q 19

The curvature of the curve given by the vector function is Use the formula to find the curvature of at the point .
A)
B)
C)
D)
E)

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Q 25Q 25

Find a vector function that represents the curve of intersection of the two surfaces: The circular cylinder and the parabolic cylinder .
A)
B)
C)
D)
E)

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Q 30Q 30

Classify the surface.
A)A circular paraboloid with vertex and axis the z-axis.
B)A hyperboloid of one sheet with center and axis parallel to the z-axis.
C)A cone with axis parallel to the z-axis and vertex .

Free

Multiple Choice

Q 31Q 31

Find an equation for the surface consisting of all points that are equidistant from the point and the plane .
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 32Q 32

Find an equation for the surface consisting of all points P for which the distance from P to the x-axis is times the distance from P to the yz-plane.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 33Q 33

Find the point at which the line given by the parametric equations below intersects the plane.
A)
B)
C)
D)
E)

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Q 36Q 36

Find an equation of the plane with x-intercept , y-intercept and z-intercept .
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 37Q 37

Find parametric equations for the line through the point that is parallel to the plane and perpendicular to the line
A)
B)
C)
D)
E)

Free

Multiple Choice

Free

Multiple Choice

Q 39Q 39

Find the distance between the point and the plane Round your answer to two decimal place.
A)
B)
C)
D)
E)

Free

Multiple Choice

Free

Essay

Free

Essay

Free

Essay

Free

Multiple Choice

Free

Multiple Choice

Q 45Q 45

Find a nonzero vector orthogonal to the plane through the points P, Q, and R.
A)
B)
C)
D)
E)None of these

Free

Multiple Choice

Q 46Q 46

Let and let u be a vector with length that starts at the origin and rotates in the xy - plane. Find the maximum value of the length of the vector .
A)
B)
C)
D)
E)

Free

Multiple Choice

Free

Essay

Q 48Q 48

A bicycle pedal is pushed by a foot with a force of a-N as shown. The shaft of the pedal is cm long.Find the magnitude of the torque about P correct to two decimal places.Let N, , .

Free

Essay

Q 49Q 49

Find the magnitude of the torque about P correct to two decimal places if a d-lb force is applied as shown. Let ft, ft, , lb.

Free

Essay

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Q 53Q 53

Calculate the angle between a and b (correct to the nearest degree).
A)
B)
C)
D)
E)None of these

Free

Multiple Choice

Q 54Q 54

Find the work done by a force that moves an object from the point to the point along a straight line. The distance is measured in meters and the force in newtons.
A)
B)
C)
D)
E)

Free

Multiple Choice

Free

Multiple Choice

Free

Multiple Choice

Q 57Q 57

Find the unit vectors that are parallel to the tangent line to the curve at the point .
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 58Q 58

A woman walks due west on the deck of a ship at mi/h. The ship is moving north at a speed of mi/h. Find the speed of the woman relative to the surface of the water. Round the result to the nearest tenth.

Free

Essay

Q 59Q 59

The tension T at each end of the chain has magnitude N and makes an angle with the horizontal. What is the weight of the chain? Round the result to the nearest hundredth.

Free

Essay

Q 60Q 60

Suppose you start at the origin, move along the x-axis a distance of units in the positive direction, and then move downward a distance of units. What are the coordinates of your position?
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 61Q 61

Find the length of each side of the triangle ABC and determine whether the triangle is an isosceles triangle, a right triangle, both, or neither.A (-1, 0, 1), B (1, 1, -1), C (1, 1, 1)
A)3, 2, , right
B)1, 1, , isosceles
C)1, 2, , neither
D)1, 1, , both

Free

Multiple Choice

Free

Multiple Choice

Q 63Q 63

Find the standard equation of the sphere with center C and radius r.C (3, -5, 3); r = 7
A)(x - 3)

^{2}+ (y + 5)^{2}+ (z - 3)^{2}= 49 B)(x - 3)^{2}+ (y + 5)^{2}+ (z - 3)^{2}= 7 C)(x + 3)^{2}+ (y - 5)^{2}+ (z + 3)^{2}= 49 D)(x + 3)^{2}+ (y - 5)^{2}+ (z + 3)^{2}= 7Free

Multiple Choice

Q 64Q 64

Find the center and the radius of the sphere that has the given equation. + + - 6x + 4y = 0
A)( 3, -2, 0), 13
C)( 3, -2, 0),
B)( -3, 2, 0),
D)( -3, 2, 0), 13

Free

Multiple Choice

Free

Multiple Choice

Q 66Q 66

Write an inequality to describe the half-space consisting of all points to the left of a plane parallel to the xz-plane and units to the right of it.

Free

Essay

Q 67Q 67

Write an inequality to describe the region consisting of all points between (but not on) the
spheres of radius and centered at the origin.

Free

Essay

Q 68Q 68

Write inequalities to describe the solid upper hemisphere of the sphere of radius centered at the origin.

Free

Essay