Vectors

Vector 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=-i+5j  and w=2i-3j

Find 3u-4w

-11i+27j

Find the Magnitude

100

Magnitude of <3,4>

5

200

Magnitude of <-1,-1>

sqrt 2

300

What is the name of Ms. Lei's cat? (Spelling counts!)

Chandler

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

Define the vectors i and j

.

300

Define a scalar

a number which has only magnitude and no direction.

400

A vector must have what two things?

direction and magnitude

500

Equal vectors have the same ________ and _______.

1. direction

2. magnitude

Find the Vector

100

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

<4,2>

200

Which football team won the Super Bowl in 2025?

the Philadelphia Eagles

300

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

<5,4>

400

Find the unit vector that has the same direction as v=-3i-4j

v=-3/5i-4/5j

500

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

<9,-11>

Dot Product

100

What does it mean if the dot product of two vectors is equal to 0?

The vectors are orthogonal (perpendicular)

200

What do you get if you dot product a vector with itself?

the magnitude squared

300

<1,1>*<2,3>

5

400

<-1,4>*<2,-3>

-14

500

<43,0>*<0,19>

0