Multiplying Vectors by Vectors: Day 3

Question 1

What are the 2 types of multiplication?

Answer 1

1) dot product
2) cross product
* produce very different results)

Question 2

What is the dot product formula?

Answer 2

a . b=|a||b|cos θ

-angle between vectors is tail to tail

Question 3

What are the properties of the dot product?

Answer 3

• result is SCALAR

- answer=0 when angle=90 (vectors are PERPENDICULAR)

Question 4

What is the dot product from the cartesian equation?

Answer 4

a . b= axbx+ayby

-produces a single number

Question 5

What are some applications of the dot product?

Answer 5

1) finding the angle between 2 vectors
2) finding the value of k when vectors are perpendicular
- set the dot product as =0 and solve for k

Question 6

What is the equation for work?

Answer 6

w=|f||s|cos θ
w-work (J)
f- force applied (N)
s- displacement (m)

Question 7

What is a projection and what is the equation for it?

Answer 7

can be thought of as “shadows”
-projection (a onto b)= |a|cos θ (1/|b|) (b)
or
-proj (a onto b)=a . b/ b. b (b)

Question 8

What is a 3D vector?

Answer 8

uses x,y and z components [1,2,3] on an x,y,z grid (z-vertical x-diagonal to the left y-diagonal to the right)

Question 9

How do you plot 3D vectors?

Answer 9

ex. [4,1,-3] move 4 on x, 1 on y and -3 on z

Question 10

How do you find the AB vector when dealing with 3D vectors?

Answer 10

find how far in x,y,z components to go from A to B (subtract A points from B points)

Question 11

What is the equation of magntiude for 3D vectors?

Answer 11

|b|=square root of x^2+y^2+z^2