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

Rays, head, tail

What are the two methods of vector addition

Head to tail method (keep parallel and same length)

Parallelogram Method

When you add two vectors, you get a ______ vector

Resultant

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

Parentheses

i’s and js

(Horizontal, vertical)

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

Positive

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

SOHCAHTOA, bearing

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

Tail, head

What is scalar multiplication?

Multiplying a scalar by a vector

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

Rotation

In the parallelogram method, you put the two tails _____

Together

A vector’s unit vector comes from the _______ ___________

Unit circle

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

Directed line segment

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

Initial, terminal (head, tail)

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

Magnitude

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

Vector

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

Magnitude, direction

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

Standard position

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

Unit vector

The two basic vector operations are scalar __________ and vector _________

Multiplication, addition

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

Resultant

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

Standard unit vector, horizontal, vertical

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

b,a

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

X

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

System of equations

The dot product yields a (scalar/number)

Scalar

The dot product is u*v=

U1*V1+U2*V2

The five vector relationships include ….

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

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

0

Work is magnitude of force * _____________ the object moves

It is a directly proportional equation

Direction

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

Dot product

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

U1*v1+u2*v2

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

U*V/IIuII*IIvII

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

Orthogonal

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

Draw

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

Use Pythagorean theorem or distance formula

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

Vector

Vectors have direction and magnitude (_______)

Length

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

Equal

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

Tan(theta)=b/a

3600sin^x+3600cos^2x=

3600(1)

The Magnitude is a _____

Number

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

Rotation