Math 2650 Quiz 2

Find the value of A so that proj v u = …

Use proj v u = dot product / magnitude of v & factor the vector

Set of points equidistant

Vector between points & midpoint, dot product those to find D & scale

Area of triangle with 3 vertices

Cross vectors w/ shared point, take magnitude, and divide by 2

Unit vector perpendicular

Cross and divide by magnitude of cross

Find distance between parallel lines

Find vector between points and coefficient vector and use d = | pq x s | / | s |

Given mag u and mag v, find cos theta

Expand w/ u*u=|u|² to isolate dot product then use cos = dot product / mag u * mag v

Find all unit vectors u given u and cos theta

Use cos = dot product / mag u * mag v and | u | = 1 to get two equations & solve variables

Triangle has vertices, find a so the triangle has area …

Find 2 vectors w/ common point, cross them, magnitude, area is ½ mag compare them (sqrt a² = | a |)

Two planes intersect at a right angle

Get point and vector from equations, cross to get n1, then n1 x v to get n2, n1 w/ origin, n2 w/ point

Point on plane closest point

Get vector from plane, create para eq of the line, plug into plane eq, find t plug back in to point