Year 12 Term 4

Question 1

Dot product formula

Answer 1

a ° b = |a| x |b| x Cos theta

Question 2

What is the cosine rule in vector form

Answer 2

|a-b|^2 = |a|^2 + |b|^2 - 2a ° b

Question 3

What is the dot product formula for components

Answer 3

u ° v = x1x2 + y1y2

Question 4

What is the rule for terms in dot product

Answer 4

I ° I = J ° J = 1

I ° J = J ° I = 0

Question 5

How can projection u onto x be expressed using dot product

Answer 5

PROJxU = (u ° x^) x^
Or
PROJxU =(u ° x/x ° x) × X

Question 6

How to test if vectors are perpendicular

Answer 6

U ° V =0

Question 7

How to test if vectors are parallel

Answer 7

U ° V = |U| |V|

Question 8

How to find direction of vector

Answer 8

Tan^-1 (y/x)

Question 9

Length of projection formula

Answer 9

PROJbA = a°b/|b|