PreCalc Chapter 6 Test Part 2 Flashcards
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=
U1V1+U2V2
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+_____________________.
U1v1+u2v2
If theta is the angle between two nonzero vectors u and v, then cos theta=
UV/IIuIIIIvII
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
