PreCalc Chapter 6 Test Part 2

Question 1

Vectors are not ______ because they do not go on forever. They have a _____, where the arrow is, and a _______

Answer 1

Rays, head, tail

Question 2

What are the two methods of vector addition

Answer 2

Head to tail method (keep parallel and same length)

Parallelogram Method

Question 3

When you add two vectors, you get a ______ vector

Answer 3

Resultant

Question 4

Component form uses _______ white standard unit vector form uses __ and __

Answer 4

Parentheses
i’s and js
(Horizontal, vertical)

Question 5

The magnitude of a vector is always _______ and is denoted using two “lines” on each side

Answer 5

Positive

Question 6

Use ________ to find direction of vectors. They can be written using _____

Answer 6

SOHCAHTOA, bearing

Question 7

When finding the horizontal and vertical distances of a vector, start at the ____ and end at the ____

Answer 7

Tail, head

Question 8

What is scalar multiplication?

Answer 8

Multiplying a scalar by a vector

Question 9

If a question asks for a direction, give the angle of ____

Answer 9

Rotation

Question 10

In the parallelogram method, you put the two tails _____

Answer 10

Together

Question 11

A vector’s unit vector comes from the _______ ___________

Answer 11

Unit circle

Question 12

A ______ _______ _______ can be used to represent a quantity that involves both magnitude and direction

Answer 12

Directed line segment

Question 13

The directed line segment PQ has _______ point P and ______ point Q

Answer 13

Initial, terminal (head, tail)

Question 14

The ______ of the directed line segment PG is donated by IIPQII

Answer 14

Magnitude

Question 15

The set of all directed line segments that are equivalent to a given directed line segment PQ is a _______ v in the plane

Answer 15

Vector

Question 16

In order to show that two vectors are equivalent, you must show that they have the same ________ and the same _________

Answer 16

Magnitude, direction

Question 17

The directed line segment whose initial point is the origin is said to be in __________ _____________

Answer 17

Standard position

Question 18

A vector that has a magnitude of 1 is called a ______ ________

Answer 18

Unit vector

Question 19

The two basic vector operations are scalar __________ and vector _________

Answer 19

Multiplication, addition

Question 20

The vector u + v is called the _______ of vector addition

Answer 20

Resultant

Question 21

The vector sum v1i +v2j is called a ________ __________ of the vectors I and j, and the scalars v1 and v2 are called the ______ and _______ components of v, respectively

Answer 21

Standard unit vector, horizontal, vertical

Question 22

In a vector [a,b], the tangent of the vector is found by taking tan(theta)=______/______

Answer 22

b,a

Question 23

When finding the angle of rotation, start at the ___ axis on the right side and rotate counterclockwise

Answer 23

X

Question 24

When adding vectors, you may have to use _____ ____ ________

Answer 24

System of equations

Question 25

The dot product yields a (scalar/number)

Answer 25

Scalar

Question 26

The dot product is u*v=

Answer 26

U1V1+U2V2

Question 27

The five vector relationships include ….

Answer 27

Opposite, obtuse angle, 90 angle (orthogonal), acute angle, same direction

Question 28

If two vectors are orthogonal, the dot product u*v=__

Answer 28

0

Question 29

Work is magnitude of force * _____________ the object moves

It is a directly proportional equation

Answer 29

Direction

Question 30

The ________ ________ of two vectors yields a scalar, rather than a vector

Answer 30

Dot product

Question 31

The dot product of u= (u1, u2) and v= (v1, v2) is u*v+_____________________.

Answer 31

U1v1+u2v2

Question 32

If theta is the angle between two nonzero vectors u and v, then cos theta=

Answer 32

UV/IIuIIIIvII

Question 33

The vectors u and v are __________ when u*v=0

Answer 33

Orthogonal

Question 34

When finding the angle between two vectors, _____ your vectors first to make sure your angle makes sense and the calculator didn’t mess it up because of the inherent restriction

Answer 34

Draw

Question 35

How do you find the magnitude of u (8,15)

Answer 35

Use Pythagorean theorem or distance formula

Question 36

To find the interior angles of the triangle with the given vertices, be careful and remember that you can’t use the same ________ sometimes

Answer 36

Vector

Question 37

Vectors have direction and magnitude (_______)

Answer 37

Length

Question 38

When finding tensions, make sure you know if they are __________ or not

Answer 38

Equal

Question 39

When asked to find the direction of the resultant vector, use __________

Answer 39

Tan(theta)=b/a

Question 40

3600sin^x+3600cos^2x=

Answer 40

3600(1)

Question 41

The Magnitude is a _____

Answer 41

Number

Question 42

When doing tensions and force questions, don’t assume the written angles are correct, you need the angle of ______

Answer 42

Rotation