Practice Multiplying Vectors

Practice with Multiplying Vectors

Fill in the Blanks

If vector X is <2,-3>

Find 2X

Be sure that your answer is in the format <_,_> That is, include the <> and the comma and do not use any spaces

Fill in the Blanks

If Vector Y is <-1,-6>

find -3Y

Be sure that your answer is in the format <_,_> That is, include the <> and the comma and do not use any spaces

Fill in the Blanks

If vector Z is <0,5>

Find -Z

Be sure that your answer is in the format <_,_> That is, include the <> and the comma and do not use any spaces

Fill in the Blanks

If vector W is <-10,8>

Find 5W

Be sure that your answer is in the format <_,_> That is, include the <> and the comma and do not use any spaces

Fill in the Blanks

If vector V is <4,5>

find -2V

Be sure that your answer is in the format <_,_> That is, include the <> and the comma and do not use any spaces

Reminder for Dot Product

Math Response

Find the dot product of these vectors

<9,6>

<5,3>

Type answer here

Correct Answer: 63

Deg^°

Rad

Math Response

Find the dot product

X <-1,5>

Y <-6,-2>

Type answer here

Correct Answer: -4

Deg^°

Rad

Math Response

Find the Dot Product of these two vectors

A <-7,-9>

B <8,4>

Type answer here

Correct Answer: -92

Deg^°

Rad

Math Response

Find the dot product

<-2,2>

<8,-1>

Type answer here

Correct Answer: -18

Deg^°

Rad

What about vectors in 3D?

Vectors in 3D don't just have an x and y component, they also have a z. Think of x as left to right, y is up and down, and z is your depth (forward and backwards)

Scalar Multiplication in

To do Scalar multiplication for 3D vectors, you "distribute" the scalar across all 3 values

Imagine that vector A is <3,-2,4>
3A would be <9,-6,12>

Fill in the Blanks

If Vector B is <1,0,-5>

Find 2B

Be sure that your answer is in the format <_,._,_> That is, include the <> and the comma and do not use any spaces

Fill in the Blanks

If vector C is <-2,-5,8>

Find -3C

Be sure that your answer is in the format <_,._,_> That is, include the <> and the comma and do not use any spaces

Dot Product of a 3D vector

The dot product of a 3D vector is found similarly to a vector in 2D space.
1. multiply the x values
2. multiply the y values
3. multiply the z values
4. add all the products

​Imagine finding the dot product of the vectors
A <1,5,-2> and B <2,-3,4>
(1*2) + (5*-3) + (-2*4)
2 + -15 + -8 = -21

Math Response

Find the dot product of

<2,2,-4>

<0,3,-7>

Type answer here

Correct Answer: 34

Deg^°

Rad

Math Response

Find the dot product

<0,-5,9>

<1,0,-6>

Type answer here

Correct Answer: -54

Deg^°

Rad