Chapter 3: Vectors

Question 1

What is a scalar quantity?

Answer 1

A quantity described by a numerical value but without an associated direction.

Question 2

What is a vector quantity?

Answer 2

A quantity with both size (magnitude) and direction.

Question 3

How is the magnitude of a vector denoted?

Answer 3

|a| (With an arrow above the vector’s symbol)

Question 4

What is a unit vector?

Answer 4

A dimensionless symbol with a magnitude equal to one, with the purpose of specifying a chosen direction.

Question 5

The unit vector ___ points in the +x direction.

Answer 5

î

Question 6

The unit vector ___ points in the +y direction.

Answer 6

ĵ

Question 7

The unit vector ___ points in the +z direction.

Answer 7

k̂

Question 8

r(arrow) = …

Answer 8

a(arrow) + b(arrow) + c(arrow)

Question 9

The r(arrow) equation above can be used to deal individually with ___ components.

Answer 9

x, y, and z

Question 10

TRUE or FALSE: Components must be dealt with separately (IE, y’s with y’s, x’s with x’s, and so on).

Answer 10

True!

Question 11

What is the definition of a scalar product?

Answer 11

a(arrow) * b(arrow) = |a(arrow)||b(arrow)|cosΦ

Question 14

The right side of the scalar product equation contains only scalars. Thus, the product produces a ___.

Answer 14

Scalar

Question 15

The scalar in a dot product can be either positive or negative depending on the sign of cosΦ, but the sign (does)/(does not) indicate a direction.

Answer 15

Does not

Question 16

You (can)/(cannot) use the larger angle between the vectors, as it (does)/(does not) have the same result.

Answer 16

Can; does

Question 17

The product is also called the “dot product” because of the center dot, and is spoken as ___ or ___.

Answer 17

“a dot b”; “a dotted into b”

Question 18

The scalar product in unit-vector notation simplifies down into:

Answer 18

a(arrow) * b(arrow) = a(subx)b(subx) + a(suby)b(suby) + a(subz)b(subz)

Question 19

A vector cross-product is written as…

Answer 19

a × b

Question 20

When doing a cross product, (a is collapsed into b)/(b is collapsed into a).

Answer 20

Vector a is collapsed into vector b.

Question 21

The direction of c, the resulting vector, is determined using the ___.

Answer 21

RHR, or right-hand rule.

Question 22

The vector product of cross products (is)/(is not) communicative.

Answer 22

Is not.