What is the x component of A⃗ ?

Ax = 2.5

What is the y component of A⃗ ?

Ay = 3

What is the x component of A⃗ ?

Ax = 2.5

What is the y component of A⃗ ?

Ay = 3

What is the y component of B⃗ ?

By = -3

What is the x component of C⃗ ?

Cx = -2

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

Bx, By = 2,-3

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

Dx, Dy = 2,-3

What is true about B⃗ and D⃗ ? 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 C⃗ =A⃗ +2B⃗

Draw the vector C⃗ =1.5A⃗ −3B⃗

Draw the vector C⃗ =0.5A⃗ +2B⃗ .

Let vectors A⃗ =(2,1,−4), B⃗ =(−3,0,1), and C⃗ =(−1,−1,2).

A⃗ ⋅B⃗ =

A⃗ ⋅B⃗ =

-10

Let vectors A⃗ =(2,1,−4), B⃗ =(−3,0,1), and C⃗ =(−1,−1,2).

What is the angle θAB between A⃗ and B⃗ ?

What is the angle θAB between A⃗ and B⃗ ?

2 radians

Let vectors A⃗ =(2,1,−4), B⃗ =(−3,0,1), and C⃗ =(−1,−1,2).

2B⃗ ⋅3C⃗ =

2B⃗ ⋅3C⃗ =

30

Let vectors A⃗ =(2,1,−4), B⃗ =(−3,0,1), and C⃗ =(−1,−1,2).

2(B⃗ ⋅3C⃗ ) =

2(B⃗ ⋅3C⃗ ) =

30

Let vectors A⃗ =(2,1,−4), B⃗ =(−3,0,1), and C⃗ =(−1,−1,2).

Which of the following can be computed?

A⃗ ⋅B⃗ ⋅C⃗

A⃗ ⋅(B⃗ ⋅C⃗ )

A⃗ ⋅(B⃗ +C⃗ )

3⋅A⃗

Which of the following can be computed?

A⃗ ⋅B⃗ ⋅C⃗

A⃗ ⋅(B⃗ ⋅C⃗ )

A⃗ ⋅(B⃗ +C⃗ )

3⋅A⃗

A⃗ ⋅(B⃗ +C⃗ )

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

V⃗ 1⋅V⃗ 2 =

V⃗ 1⋅V⃗ 2 =

V1V2

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

If V⃗ 1 and V⃗ 2 are parallel, V⃗ 1⋅V⃗ 2 =

If V⃗ 1 and V⃗ 2 are parallel, V⃗ 1⋅V⃗ 2 =

V1V2

Let vectors A⃗ =(1,0,−3), B⃗ =(−2,5,1), and C⃗ =(3,1,1).

B⃗ ×C⃗ =

B⃗ ×C⃗ =

4,5,-17

Let vectors A⃗ =(1,0,−3), B⃗ =(−2,5,1), and C⃗ =(3,1,1).

C⃗ ×B⃗ =

C⃗ ×B⃗ =

-4,-5,17

Let vectors A⃗ =(1,0,−3), B⃗ =(−2,5,1), and C⃗ =(3,1,1).

(2B⃗ )×(3C⃗ ) =

(2B⃗ )×(3C⃗ ) =

24,30,-102

Let vectors A⃗ =(1,0,−3), B⃗ =(−2,5,1), and C⃗ =(3,1,1).

A⃗ ×(B⃗ ×C⃗ ) =

A⃗ ×(B⃗ ×C⃗ ) =

15,5,5

Let vectors A⃗ =(1,0,−3), B⃗ =(−2,5,1), and C⃗ =(3,1,1).

A⃗ ⋅(B⃗ ×C⃗ ) =

A⃗ ⋅(B⃗ ×C⃗ ) =

55

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

If V⃗ 1 and V⃗ 2 are perpendicular,

|V⃗ 1×V⃗ 2| =

If V⃗ 1 and V⃗ 2 are perpendicular,

|V⃗ 1×V⃗ 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

0

10

5

-5

0

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