Vectors

Question 1

What is the vector equation of a line

Answer 1

r= OA + lambda AB

Question 2

How do you make the vector equation of a line cartesian

Answer 2

Create parametric then turn into cartesian

Question 3

What do you do if one or two of d1,2,3 are zero

Answer 3

Separate equations

X=a, lambda y = lambda z
Or
x=a , y= b

Question 4

What is the equation of a plane

Answer 4

r= OA + lambda AB + ų AC

Question 5

Cartesian of the equation of a plane

Answer 5

Create parametric and manipulate equations to get lambda and ų by themselves and sub back in to get an equation with only x,y,z

Question 6

What is the general cartesian equation and how can we get this easier?

Answer 6

n1X + n2y + n3Z + d = 0
where d= -n•a

Coefficients can be found with vector product rule

Question 7

How do you find the angle between 2 vectors?

Answer 7

Cosine rule
Cosx = (a1b1 + a2b2)/ |OA||OB|
where vector1= (a1,b1) and vector2=(a2,b2)

Question 8

How do you find the angle between 2 vectors for 3d vectors?

Answer 8

Cosx = (a1b1 + a2b2 + a3b3)/ |OA||OB|

Question 9

How do you find the scalar factor?

Answer 9

(X,y,z) • (a,b,c) = xa + yb + zc

Question 11

At what value of theta are a and b perpendicular

Answer 11

Theta= 90 degrees and a•b= 0