Calc 2 Vectors & Parametrics

Distance between Point P and Plane passing through point Q with normal vector N

|QP*N|/‖N‖

Distance between Line and point M given Line going through point P and v = Direction vector

‖PM x v‖/‖v‖

Projection of v on to u (PROJuV

(uv)/‖u‖^2u

Standard Unit Vector

ai+bj+ck

Component form of vector

<x, y, z>

symmetric equations of line L

(x - x0)/v0 = (y - y0)/v1 = (z - z0)/v2

Vector equation of a Line

L = Position Vector P + t(direction vector v)

angle formula

(uv)/(‖u‖‖v‖) = cos(theta)

Parametric Equations

x = x0 + tv0, y = y0 + tv1, z = z0 + tv2

What is a normal vector

The orthogonal/perpendicular cross product of two vectors on a plane.

Unit vector in the direction u given vector u

u^ = u / ‖u‖

Equation of Plane given Normal Vector N = <v0, v1, v2> and point P = <x0, y0, z0>

[v0*<x - x0>] + [v1*<y - y0)] + [v2*<z - z0>] = 0

MUST WRITE “= 0” or minus credit