PreCalc Chapter 6 Test Part 2 Flashcards

1
Q

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

A

Rays, head, tail

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2
Q

What are the two methods of vector addition

A

Head to tail method (keep parallel and same length)

Parallelogram Method

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3
Q

When you add two vectors, you get a ______ vector

A

Resultant

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4
Q

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

A

Parentheses
i’s and js
(Horizontal, vertical)

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5
Q

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

A

Positive

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6
Q

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

A

SOHCAHTOA, bearing

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7
Q

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

A

Tail, head

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8
Q

What is scalar multiplication?

A

Multiplying a scalar by a vector

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9
Q

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

A

Rotation

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10
Q

In the parallelogram method, you put the two tails _____

A

Together

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11
Q

A vector’s unit vector comes from the _______ ___________

A

Unit circle

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12
Q

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

A

Directed line segment

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13
Q

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

A

Initial, terminal (head, tail)

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14
Q

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

A

Magnitude

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15
Q

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

A

Vector

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16
Q

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

A

Magnitude, direction

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17
Q

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

A

Standard position

18
Q

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

A

Unit vector

19
Q

The two basic vector operations are scalar __________ and vector _________

A

Multiplication, addition

20
Q

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

21
Q

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

A

Standard unit vector, horizontal, vertical

22
Q

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

23
Q

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

24
Q

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

A

System of equations

25
The dot product yields a (scalar/number)
Scalar
26
The dot product is u*v=
U1*V1+U2*V2
27
The five vector relationships include ....
Opposite, obtuse angle, 90 angle (orthogonal), acute angle, same direction
28
If two vectors are orthogonal, the dot product u*v=__
0
29
Work is magnitude of force * _____________ the object moves | It is a directly proportional equation
Direction
30
The ________ ________ of two vectors yields a scalar, rather than a vector
Dot product
31
The dot product of u= (u1, u2) and v= (v1, v2) is u*v+_____________________.
U1*v1+u2*v2
32
If theta is the angle between two nonzero vectors u and v, then cos theta=
U*V/IIuII*IIvII
33
The vectors u and v are __________ when u*v=0
Orthogonal
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
Draw
35
How do you find the magnitude of u (8,15)
Use Pythagorean theorem or distance formula
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
Vector
37
Vectors have direction and magnitude (_______)
Length
38
When finding tensions, make sure you know if they are __________ or not
Equal
39
When asked to find the direction of the resultant vector, use __________
Tan(theta)=b/a
40
3600sin^x+3600cos^2x=
3600(1)
41
The Magnitude is a _____
Number
42
When doing tensions and force questions, don't assume the written angles are correct, you need the angle of ______
Rotation