Vectors

Vector Operations

100

<2,3> + <1,4>

What is <3,7>?

200

u = <-2,3>

2u

What is <-4, 6>?

300

(-2i+6j) + (4i-j)

What is 2i+5j?

400

u = <2,2>  v = <1,3>

3u + 2v

What is <8,12>?

500

u = <5, -7>

-u

What is <-5, 7>?

Find the Magnitude

100

Magnitude of <3,4>

What is 5?

200

Magnitude of <-1,-1>

What is √2?

300

This is the length of a vector.

What is the magnitude?

400

Magnitude of 5i+12j

What is 13?

500

Magnitude of 7j

What is 7?

General

100

When a vector is written as a linear combination, the letters i and j have a magnitude of 1 and they have these two directions.

horizontal (i) and vertical (j)

200

Every vector has these two properties.

What are magnitude and direction?

300

Scalar quantity. 

A quantity that has magnitude or size but no direction. 

400

True or False?  The dot product is a vector.

What is false?

500

If given the magnitude and direction of a vector, these two formulas are used to find the components of the vector.

What are  |v|cos(theta) and |v|sin(theta)?

Find the Vector

100

Vector from (0,0) to (4,2)

What is <4,2>?

200

A vector with magnitude of 10 and direction of 220^o

What is <10cos220, 10sin220>?

300

Vector from (-2,0) to (3,4)

What is <5,4>?

400

Vector from (3,3) to (0,1)

What is <-3,-2>?

500

Vector from (-2,10) to (7,-1)

What is <9,-11>?

Dot Product

100

The term that means the dot product of two vectors is equal to 0.

What is orthogonal (perpendicular)?

200

What you get if you dot product a vector with itself.

What is the magnitude squared?

300

The dot product of <1,1> and <2,3>.

What is 5?

400

The dot product of <-1,4> and <2,-3>.

What is -14?

500

The angle between the vectors <43,0> and <0,19>.

What is 90 degrees?