Final Exam

Question 1

Angle between vectors CA and CB

Answer 1

CA * CB = ||CA|| * ||CB|| * cos(x) where x is the angle in question

Question 2

||x|| =

Answer 2

sqrt(x1^2 + x2^2 + x3^2) or sqrt(x * x)

Question 3

Volume of a parallelopiped

Answer 3

a * (b x c)

Question 4

Equivalent method of writing a x b

Answer 4

-b x a

Question 5

Is cross product distributive?

Answer 5

Yes. a x (b + c) = a x b + a x c

Question 6

Distance to a plane from a point off that plane

Answer 6

d = (Ax * n) / ||n|| where n is the vector normal to the plane, A is a point on the plane, and x is the point being measured from.

Question 7

Equation of a plane

Answer 7

ax + by + cz = D. Incidentally, D is the distance from the origin.

Question 8

finding the equation of a plane

Answer 8

a(x - x0) + b(y - y0) + c(z - z0) = 0