Final

Question 1

Dot Product Theorem (find angle between vectors)

Answer 1

u ⋅ v =|u||v|cosθ

Question 2

Scalar Projection (u on v and v on u)

Answer 2

u on v:
comp v^u = (u ⋅ v)/|v|

v on u:
comp u^v = (u ⋅ v)/|u|

Question 3

Vector Projection (u on v and v on u)

Answer 3

u on v:
proj v^u = ((u ⋅ v)/|v|^2) v

v on u:
proj u^v = ((u ⋅ v)/|u|^2) u

Question 4

Orthogonal Projection of u

Answer 4

orth v^u = u - proj v^u

Question 5

Dot Product is orthogonal (90 degrees) when…

Answer 5

it equals 0

Question 6

Vector u x v is _ to both u and v

Answer 6

orthogonal

Question 7

u x u =

Answer 7

0

Question 8

Cross Product Theorem (angle between)

Answer 8

|u x v| = |u||v|sinθ

Question 9

Cross Product is parallel when

Answer 9

it equals 0

Question 10

Area of a parallelogram =

Answer 10

|u x v|

Question 11

Area of triangle

Answer 11

1/2(Area of paralelogram)

Question 12

Equation of a line

Answer 12

r(t) = r0(t) + vt

Question 13

Equation of a plane

Answer 13

n ⋅ < x - x0, y - y0, z - z0 >

Question 14

Two planes are parallel when…

Answer 14

their normal vectors are also parallel

Question 15

Complete seperate flashcards for cylinders or surfaces

Question 16

Differenteration Rules for Cross Product