Vectors Precalc A

Operations

100

<2,3> + <1,4>

<3,7>

200

2 <-2,3>

<-4, 6>

300

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

2i+5j

400

3<2,2> + 2<1,3>

<8,12>

500

Let u=<3,5> and v=<-2,1>. What is u·v?

-1

Magnitude

100

Magnitude of <3,4>

5

200

Magnitude of <-1,-1> as a simplified root.

sqrt 2

300

Find the magnitude: <3,2> + <-3,4>

6

400

Magnitude of 5i+12j

13

500

Magnitude of 7j

7

General

100

What's the definition of a unit vector?

A vector with magnitude equal to one.

200

How can I check if two vectors are orthogonal? 

See if the dot product is 0.

300

Define a scalar

Any real number that can be used to "scale", such as 2, 5, pi, 1/2, etc. 

400

A vector must have what two things?

direction and magnitude

500

Graphically, what happens when I multiply a vector by -2? 

The vector goes in the opposite direction and doubles in length.

Find the Vector

100

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

<4,2>

200

From (-2, 0) to (-7, -1)

<-5, -1>

300

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

<5,4>

400

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

<-3,-2>

500

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

<9,-11>

Vector and Dot Product Applications

100

Find the magnitude: (2, 3) to (-3, 6). Answer as a square root.

√34

200

Find the directional angle of <27,33>. Round to the tenth.

50.7°

300

Find the Magnitude and direction: (0,2) to (-4, 1)

||v|| = √17 or 4.1,  Angle = 194.0°

400

Find the Magnitude and Direction of <0, 5>

||v|| = 5,  Angle = 90

500

Find the angle between the vectors <2,5> and <3,4>. Round to the tenth.

15.1°