Exam 1 formulas

Question 1

Ideal Projectile Motion

Answer 1

r(t) = (|Vo|cos(ø)t)i + (|Vo|sin(ø)t - 1/2 gt^2)j

Question 2

Vector projection

Answer 2

Proj v u = (u . v / |v|^2 * v)
(projection of u onto v)

Question 3

Angle between two vectors

Answer 3

(comes from dot product definition)

cos^-1 ( u . v / |u| |v| )

Question 4

Midpoint

Answer 4

(x1+x2/2, y1+y2/2, z1+z2/2)

Question 5

Distance between a point and a plane

Answer 5

d = IAx + By + Cz + DI / √ (A² + B² + C²)

Question 6

Distance between two planes

Answer 6

d = | PS . n/|n| |

Question 7

Arc Length

Answer 7

integral from a to b of (√((dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2))) dt

Question 8

Cross Product

Answer 8

determinant of matrix of two vectors

i. j. k.
x y. z
x y. z

Question 9

Dot Product

Answer 9

|u . v| = |u||v|cos(ø)

|u . v|= (ux * vx)+(uy * vy)+(uz * vz)

Question 10

Equation for a plane

Answer 10

A(X-Xo)+B(Y-Yo)+C(Z-Zo)=0

Question 11

Volume of a parrallelepipped

Answer 11

|u x v||w|cos(ø)

Question 12

Unit Tangent Vector (T)

Answer 12

T = V/|V|

Question 13

Curvature of a curve

Answer 13

k = 1/|V| * |dT/dt|

Question 14

Principal Unit Normal Vector

Answer 14

N = (dT/dt)/(|dT/dt|)

Question 15

Tangential Acceleration

Answer 15

aT = d/dt |v|

Question 16

Normal Acceleration

Answer 16

k|v|^2. or sqrt(|a|^2-aT^2)

Question 17

Distance from a point to a line

Answer 17

d = |Ax + By + C| / sqrt(A² + B²)

Question 18

Area of a triangle

Answer 18

1/2 |AB x AC|

Question 19

Area of a Parallelogram

Answer 19

|AB x AC|

Question 20

Triple scalar

Answer 20

|w1 w2 w3 |
|u1 u2 u3 |
|v1 v2 v3 |