Vectors

Question 1

Scalar dot product

Answer 1

a.b = |a||b|cosx
a.b = 0 if a and b are perp

Question 2

Vector line equation

Answer 2

r_ = a_ + sigma b_

Question 3

Cartesian line equations

Answer 3

lambda = (x-a1)/b1, etc for y and z increasing numbers

Question 4

Vector intersections between two lines

Answer 4

Check if parallel.
If not parallel, check if intersecting by simultaneous equations.
If not, they are skew

Question 5

How to prove dot product angle thing

Answer 5

Triangle with vectors then cosine rule

Question 6

Cross product formula

Answer 6

(A2B3 - A3B2) +
(A3B1 - A1B3) +
(A1B2 - A2B1)

Question 7

Angle between two vectors formula

Answer 7

cosx = (a.b)/|A||B|