# Mastering Physics 1

What is the x component of A? ?

Ax = 2.5

What is the y component of A? ?

Ay = 3

What is the y component of B? ?

By = -3

What is the x component of C? ?

Cx = -2

In ordered pair notation, write down the components of vector B? .

Bx, By = 2,-3

In ordered pair notation, write down the components of vector D? .

Dx, Dy = 2,-3

What is true about B? and D? ? Choose from the pulldown list below.

-They are the same vectors

-They have different components and are not the same vectors

-They have the same components but are not the same vectors.

-They are the same vectors

-They have different components and are not the same vectors

-They have the same components but are not the same vectors.

-They are the same vectors

Rank the vector combinations on the basis of their magnitude.

A+C, A+B, A+D, A+E, F+C, D

A+C, A+B, A+D, A+E, F+C, D

A+C> A+B =A+D > D =F+C >A+E

Rank the vector combinations on the basis of their angle, measured counterclockwise from the positive x axis. Vectors parallel to the positive x axis have an angle of 0? . All angle measures fall between 0? and 360?

A+C, A+B, A+D, A+E, F+C, D

A+C, A+B, A+D, A+E, F+C, D

A+B>F+C=D>A+D>A+E=A+C

Draw the vector C? =A? +2B?

Draw the vector C? =1.5A? ?3B?

Draw the vector C? =0.5A? +2B? .

Let vectors A? =(2,1,?4), B? =(?3,0,1), and C? =(?1,?1,2).

A? ?B? =

A? ?B? =

-10

Let vectors A? =(2,1,?4), B? =(?3,0,1), and C? =(?1,?1,2).

What is the angle ?AB between A? and B? ?

What is the angle ?AB between A? and B? ?

2 radians

Let vectors A? =(2,1,?4), B? =(?3,0,1), and C? =(?1,?1,2).

2B? ?3C? =

2B? ?3C? =

30

Let vectors A? =(2,1,?4), B? =(?3,0,1), and C? =(?1,?1,2).

2(B? ?3C? ) =

2(B? ?3C? ) =

30

Let vectors A? =(2,1,?4), B? =(?3,0,1), and C? =(?1,?1,2).

Which of the following can be computed?

A? ?B? ?C?

A? ?(B? ?C? )

A? ?(B? +C? )

3?A?

Which of the following can be computed?

A? ?B? ?C?

A? ?(B? ?C? )

A? ?(B? +C? )

3?A?

A? ?(B? +C? )

V? 1 and V? 2 are different vectors with lengths V1 and V2 respectively. Find the following:

V? 1?V? 2 =

V? 1?V? 2 =

V1V2

V? 1 and V? 2 are different vectors with lengths V1 and V2 respectively. Find the following:

If V? 1 and V? 2 are parallel, V? 1?V? 2 =

If V? 1 and V? 2 are parallel, V? 1?V? 2 =

V1V2

Let vectors A? =(1,0,?3), B? =(?2,5,1), and C? =(3,1,1).

B? ×C? =

B? ×C? =

4,5,-17

Let vectors A? =(1,0,?3), B? =(?2,5,1), and C? =(3,1,1).

C? ×B? =

C? ×B? =

-4,-5,17

Let vectors A? =(1,0,?3), B? =(?2,5,1), and C? =(3,1,1).

(2B? )×(3C? ) =

(2B? )×(3C? ) =

24,30,-102

Let vectors A? =(1,0,?3), B? =(?2,5,1), and C? =(3,1,1).

A? ×(B? ×C? ) =

A? ×(B? ×C? ) =

15,5,5

Let vectors A? =(1,0,?3), B? =(?2,5,1), and C? =(3,1,1).

A? ?(B? ×C? ) =

A? ?(B? ×C? ) =

55

V? 1 and V? 2 are different vectors with lengths V1 and V2 respectively. Find the following, expressing your answers in terms of given quantities.

If V? 1 and V? 2 are perpendicular,

|V? 1×V? 2| =

If V? 1 and V? 2 are perpendicular,

|V? 1×V? 2| =

V1V2

2,1,3

6.3,-0.25

cm/yr

cm/yr

y=0.6 (couldn’t get the picture, sorry!)

CBDA

-10

-5

10

5

-5

10

5

5

Referring again to the graph in Part E, rank, in increasing order, the derivatives of the function at each of the points A through E. If two of the values are equal, you may list them in either order.

CDBEA