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

u = 2i + 3j

v = 5j

w = 2i

4u - 3v + 5w

18i -3j

Magnitude & Unit Vectors

100

Magnitude of <3,4>

5

200

Magnitude of 5i+12j

13

300

Magnitude of 7j

7

400

Find a unit vector in the same direction as <-4, 3>

<-4/5, 3/5>

500

Find a unit vector in the same direction as <2, 7>

<2root53/53, 2root53/53>

or <0.275, 0.275>

General

100

What's the definition of a unit vector?

A vector with magnitude equal to one.

200

What type of angle will be between two vectors that have a negative dot product?

obtuse

300

True or False

A scalar has a direction, but no magnitude

False

400

Draw any vector v that starts at the origin and points into quadrant 2.

Then draw -3v

I will check your answers manually...

500

Draw the vectors:

 u = <3, 2> 

v = <-1, 5>s

and u - v

A picture...I will check your answers visually

Writing Vectors & Angles

100

Write the vector from (0,0) to (4,2) in component form

<4,2>

200

Write the vector from (3,3) to (0,1) in linear combination form.

-3i -2j

300

Write the vector from (-2,0) to (3,4) in component form.

<5,4>

400

Find the angle between the two vectors:

u = 7i + 1j

v = 5i + 5j

36.9 degrees

500

Find the angle between the two vectors:

u = <1, -2>

v = <-2, 1>

143 degrees

Dot Product

100

What does it mean about the direction of the vectors if the dot product = 1

The vectors are in opposite directions

The angle between them is 180 degrees

200

<43,0>dot<0,19>

0

300

<1,1>dot<2,3>

5

400

u = <-1, 4>

v = <6, 7>

Find 4u dot 2v

176

500

u = <-1, 4>

v = <6, 7>

Find (u dot v)v

<132, 154>