Question 1

A vector in the xy plane has a magnitude of 25 and an x component of 12.The angle it makes with the positive x axis is:

Accepted Answer

A) 26$\degree$ 
B) 29$\degree$ 
C) 61$\degree$ 
D) 64$\degree$ 
E) 241$\degree$ 
A) 26$\degree$ 
B) 29$\degree$ 
C) 61$\degree$ 
D) 64$\degree$ 
E) 241$\degree$ C

Question 2

A certain vector in the xy plane has an x component of 4 m and a y component of 10 m.It is then rotated in the xy plane so its x component is doubled.Its new y component is about:

Accepted Answer

A) 20 m 
B) 7.2 m 
C) 5.0 m 
D) 4.5 m 
E) 2.2 m 
A) 20 m 
B) 7.2 m 
C) 5.0 m 
D) 4.5 m 
E) 2.2 m B

Question 3

If and neither nor vanish, then:

Accepted Answer

A) and are parallel and in the same direction 
B) and are parallel and in opposite directions 
C) the angle between and is 45$\degree$ 
D) the angle between and is 60$\degree$ 
E) is perpendicular to 
A) and are parallel and in the same direction 
B) and are parallel and in opposite directions 
C) the angle between and is 45$\degree$ 
D) the angle between and is 60$\degree$ 
E) is perpendicular to A

Question 4

In the diagram, has magnitude 12 m and has magnitude 8 m.The x component of is about:

Accepted Answer

A) 1.5 m 
B) 4.5 m 
C) 12 m 
D) 15 m 
E) 20 m 
A) 1.5 m 
B) 4.5 m 
C) 12 m 
D) 15 m 
E) 20 m

Question 5

The vectors , , and are related by .Which diagram below illustrates this relationship?

Accepted Answer

A) I. 
B) II. 
C) III. 
D) IV. 
E) None of these 
A) I. 
B) II. 
C) III. 
D) IV. 
E) None of these

Question 6

Two vectors lie with their tails at the same point.When the angle between them is increased by 20$\degree$ their scalar product has the same magnitude but changes from positive to negative.The original angle between them was:

Accepted Answer

A) 0° 
B) 60$\degree$ 
C) 70$\degree$ 
D) 80$\degree$ 
E) 90$\degree$ 
A) 0° 
B) 60$\degree$ 
C) 70$\degree$ 
D) 80$\degree$ 
E) 90$\degree$

Question 7

If = (2 m)− (3 m)and = (1 m)− (2 m), then =

Accepted Answer

A) (1 m) 
B) (−1 m) 
C) (4 m)− (7 m) 
D) (4 m)+ (1 m) 
E) (−4 m)+ (7 m) 
A) (1 m) 
B) (−1 m) 
C) (4 m)− (7 m) 
D) (4 m)+ (1 m) 
E) (−4 m)+ (7 m)

Question 8

If the magnitude of the sum of two vectors is greater than the magnitude of either vector, then:

Accepted Answer

A) the scalar product of the vectors must be negative 
B) the scalar product of the vectors must be positive 
C) the vectors must be parallel and in opposite directions 
D) the vectors must be parallel and in the same direction 
E) none of the above 
A) the scalar product of the vectors must be negative 
B) the scalar product of the vectors must be positive 
C) the vectors must be parallel and in opposite directions 
D) the vectors must be parallel and in the same direction 
E) none of the above

Question 9

The two vectors (3 m)− (7 m)and (2 m)+ (3 m)− (2 m)define a plane (it is the plane of the triangle with both tails at one vertex and each head at one of the other vertices).Which of the following vectors is perpendicular to the plane?

Accepted Answer

A) (14 m)+ (6 m)+ (23 m) 
B) (−14 m)+ (6 m)+ (23 m) 
C) (14 m)− (6 m)+ (23 m) 
D) (14 m)+ (6 m)− (23 m) 
E) (14 m)+ (6 m) 
A) (14 m)+ (6 m)+ (23 m) 
B) (−14 m)+ (6 m)+ (23 m) 
C) (14 m)− (6 m)+ (23 m) 
D) (14 m)+ (6 m)− (23 m) 
E) (14 m)+ (6 m)

Question 10

The angle between = (25 m)+ (45 m)and the positive x axis is:

Accepted Answer

A) 29$\degree$ 
B) 61$\degree$ 
C) 151$\degree$ 
D) 209$\degree$ 
E) 241$\degree$ 
A) 29$\degree$ 
B) 61$\degree$ 
C) 151$\degree$ 
D) 209$\degree$ 
E) 241$\degree$

Question 11

Let = (1 m)+ (2 m)+ (2 m)and = (3 m)+ (4 m).The angle between these two vectors is given by:

Accepted Answer

A) cos-1(14/15) 
B) cos-1(11/225) 
C) cos-1(104/225) 
D) cos-1(11/15) 
E) cannot be found since and do not lie in the same plane 
A) cos-1(14/15) 
B) cos-1(11/225) 
C) cos-1(104/225) 
D) cos-1(11/15) 
E) cannot be found since and do not lie in the same plane

Question 12

Let = (2 m)+ (6 m)- (3 m)and = (4 m)+ (2 m)+ (1 m).The vector difference is:

Accepted Answer

A) (6 m)+ (8 m)- (2 m) 
B) (−2 m)+ (4 m)- (4 m) 
C) (2 m)− (4 m)+ (4 m) 
D) (8 m)+ (12 m)- (3 m) 
E) none of these 
A) (6 m)+ (8 m)- (2 m) 
B) (−2 m)+ (4 m)- (4 m) 
C) (2 m)− (4 m)+ (4 m) 
D) (8 m)+ (12 m)- (3 m) 
E) none of these

Question 13

Vectors and lie in the xy plane.We can deduce that if:

Accepted Answer

A) Ax2 + Ay2 = Bx2 + By2 
B) Ax + Ay = Bx + By  
C) Ax = Bx and Ay = By  
D) Ay /Ax = By /Bx  
E) Ax = Ay and Bx = By  
A) Ax2 + Ay2 = Bx2 + By2 
B) Ax + Ay = Bx + By  
C) Ax = Bx and Ay = By  
D) Ay /Ax = By /Bx  
E) Ax = Ay and Bx = By

Question 14

Two vectors lie with their tails at the same point.When the angle between them is increased by 20$\degree$ the magnitude of their vector product doubles.The original angle between them was about:

Accepted Answer

A) 0° 
B) 18$\degree$ 
C) 25$\degree$ 
D) 45$\degree$ 
E) 90$\degree$ 
A) 0° 
B) 18$\degree$ 
C) 25$\degree$ 
D) 45$\degree$ 
E) 90$\degree$

Question 15

Which of the following is correct?

Accepted Answer

A) Multiplying a vector by a scalar gives a scalar result. 
B) Multiplying a vector by a vector always gives a vector result. 
C) Multiplying a vector by a vector never gives a scalar result. 
D) The only type of vector multiplication that gives a scalar result is the dot product. 
E) The only type of vector multiplication that gives a vector result is the cross product. 
A) Multiplying a vector by a scalar gives a scalar result. 
B) Multiplying a vector by a vector always gives a vector result. 
C) Multiplying a vector by a vector never gives a scalar result. 
D) The only type of vector multiplication that gives a scalar result is the dot product. 
E) The only type of vector multiplication that gives a vector result is the cross product.

Question 16

If = (6 m)- (8 m)then has magnitude:

Accepted Answer

A) -8 m 
B) 8 m 
C) 10 m 
D) 40 m 
E) 56 m 
A) -8 m 
B) 8 m 
C) 10 m 
D) 40 m 
E) 56 m

Question 17

Two vectors have magnitudes of 10 and 15.The angle between them when they are drawn with their tails at the same point is 65$\degree$.The component of the longer vector along the line of the shorter is:

Accepted Answer

A) 0 
B) 4.2 
C) 6.3 
D) 9.1 
E) 14 
A) 0 
B) 4.2 
C) 6.3 
D) 9.1 
E) 14

Question 18

If the magnitude of the sum of two vectors is less than the magnitude of either vector, then:

Accepted Answer

A) the scalar product of the vectors must be negative 
B) the scalar product of the vectors must be positive 
C) the vectors must be parallel and in opposite directions 
D) the vectors must be parallel and in the same direction 
E) none of the above 
A) the scalar product of the vectors must be negative 
B) the scalar product of the vectors must be positive 
C) the vectors must be parallel and in opposite directions 
D) the vectors must be parallel and in the same direction 
E) none of the above

Question 19

Let = (2 m)+ (6 m)- (3 m)and = (4 m)+ (2 m)+ (1 m).The vector sum is:

Accepted Answer

A) (6 m)+ (8 m)- (2 m) 
B) (−2 m)+ (4 m)- (4 m) 
C) (2 m)− (4 m)+ (4 m) 
D) (8 m)+ (12 m)- (3 m) 
E) none of these 
A) (6 m)+ (8 m)- (2 m) 
B) (−2 m)+ (4 m)- (4 m) 
C) (2 m)− (4 m)+ (4 m) 
D) (8 m)+ (12 m)- (3 m) 
E) none of these

Question 20

A vector of magnitude 3 CANNOT be added to a vector of magnitude 4 so that the magnitude of the resultant is:

Accepted Answer

A) 0 
B) 1 
C) 3 
D) 5 
E) 7 
A) 0 
B) 1 
C) 3 
D) 5 
E) 7

Exam 3: Vector

A vector in the xy plane has a magnitude of 25 and an x component of 12.The angle it makes with the positive x axis is:

A certain vector in the xy plane has an x component of 4 m and a y component of 10 m.It is then rotated in the xy plane so its x component is doubled.Its new y component is about:

If and neither nor vanish, then:

In the diagram, has magnitude 12 m and has magnitude 8 m.The x component of is about:

The vectors , , and are related by .Which diagram below illustrates this relationship?

Two vectors lie with their tails at the same point.When the angle between them is increased by 20 °\degree° their scalar product has the same magnitude but changes from positive to negative.The original angle between them was:

If = (2 m)− (3 m)and = (1 m)− (2 m), then =

If the magnitude of the sum of two vectors is greater than the magnitude of either vector, then:

The two vectors (3 m)− (7 m)and (2 m)+ (3 m)− (2 m)define a plane (it is the plane of the triangle with both tails at one vertex and each head at one of the other vertices).Which of the following vectors is perpendicular to the plane?

The angle between = (25 m)+ (45 m)and the positive x axis is:

Let = (1 m)+ (2 m)+ (2 m)and = (3 m)+ (4 m).The angle between these two vectors is given by:

Let = (2 m)+ (6 m)- (3 m)and = (4 m)+ (2 m)+ (1 m).The vector difference is:

Vectors and lie in the xy plane.We can deduce that if:

Two vectors lie with their tails at the same point.When the angle between them is increased by 20 °\degree° the magnitude of their vector product doubles.The original angle between them was about:

Which of the following is correct?

If = (6 m)- (8 m)then has magnitude:

Two vectors have magnitudes of 10 and 15.The angle between them when they are drawn with their tails at the same point is 65 °\degree° .The component of the longer vector along the line of the shorter is:

If the magnitude of the sum of two vectors is less than the magnitude of either vector, then:

Let = (2 m)+ (6 m)- (3 m)and = (4 m)+ (2 m)+ (1 m).The vector sum is:

A vector of magnitude 3 CANNOT be added to a vector of magnitude 4 so that the magnitude of the resultant is:

Measurement

Motion Along a Straight Line

Motion in Two and Three Dimensions

Force and Motion I

Force and Motion II

Kinetic Energy and Work

Potential Energy and Conservation of Energy

Center of Mass and Linear Momentum

Rotation

Rolling, Torque, and Angular Momentum

Equilibrium and Elasticity

Gravitation

Fluids

Oscillations

Waves I

Waves II

Temperature, Heat, and the First Law of Thermodynamics

The Kinetic Theory of Gases

Entropy and the Second Law of Thermodynamics

Electric Charge

Electric Fields

Gauss Law

Electric Potential

Capacitance

Current and Resistance

Circuits

Magnetic Fields

Magnetic Fields Due to Currents

Induction and Inductance

Electromagnetic Oscillations and Alternating Current

Maxwells Equations; Magnetism of Matter

Electromagnetic Waves

Images

Interference

Diffraction

Relativity

Photons and Matter Waves

More About Matter Waves

All About Atoms

Conduction of Electricity in Solids

Nuclear Physics

Energy From the Nucleus

Quarks, Leptons, and the Big Bang

Filters

Two vectors lie with their tails at the same point.When the angle between them is increased by 20 $\degree$ their scalar product has the same magnitude but changes from positive to negative.The original angle between them was:

Two vectors lie with their tails at the same point.When the angle between them is increased by 20 $\degree$ the magnitude of their vector product doubles.The original angle between them was about:

Two vectors have magnitudes of 10 and 15.The angle between them when they are drawn with their tails at the same point is 65 $\degree$ .The component of the longer vector along the line of the shorter is: