Cheat Sheet

Question 1

Unit vector =

Answer 1

V/|V|

Question 2

Vector direction

Answer 2

|AB||AC|cos(O)=AB * AC

Question 3

Projection (a on to b)

Answer 3

proj(b) a = b ((a * b)/|b|^2)

Question 4

Volume of parallelpiped

Answer 4

|(a * (b x c))|

Question 5

Vector area =

Answer 5

1/2 |a x b|

Question 6

Equation of the plane (method)

Answer 6

a(x - x0) + b(y - y0) + c(z - z0) = 0
(find normal vector n=<a, b, c>
A=(x0,y0,z0)
and plug into equation)

Question 7

Parallel planes have the same ___

Answer 7

normal vector (n) = (a x b)

Question 8

Parametric equations

Answer 8

T(tangent line) = < m1, m2, m3>
x(t) = x0 + mx(t)

Question 9

Equation of a sphere (method)

Answer 9

(x-h)^2 + (y-k)^2 + (z-l)^2 = R^2
center = (h,k,l)
R = radius
(method- reverse the equation and combine x^2 + x into (x-h)^2 and add remaining onto radius)

Question 10

Motion in space (method)

Answer 10

(v’(t) = a(t); r’(t) = v(t)
v(t) = i + j + k + c
v(0) = 0 + 0 + 0 + C = C value

Question 11

T(t)- tangent line

Answer 11

r’(t)/ |r’(t)|

Question 12

N(t)- unit normal vector

Answer 12

T’(t) / |T’(t)|

Question 13

k(t)- curvature

Answer 13

|r’(t) x r’‘(t)|/(|r’(t)|^3)

Question 14

Projectile motion equations

Answer 14

x(t) = (v0 cos(O))t
y(t) = (v0 sin(O))t
d=(v0 cos(O))t (2v0 sin(O)/g)

Question 15

Equation of tangent plane (method)

Answer 15

find fx(x0,y0,z0) = a, fy(x0,y0,z0) = b, fz(x0,y0,z0) = c
and plug into: a(x-x0) + b(y-y0) + c(z-z0)

Question 16

Linearization (L(x,y)) =
(a,b,c)

Answer 16

= f(x,y) + fx(x,y)(x-a) + fy(x,y)(y-b)