#### Question

# How to do this vector problem?

Let A = (5,1,3), B = (-3,-1,3), and p=(k,k,k). The vector from A to B is perpindicular to A to P when k is equal to what number?

Thanks

#### Answers

Vector AB = ( -3 - 5, -1 -1, 3 - 3) = ( -8, -2, 0 )

Vector AP = ( k - 5, k - 1, k - 3 )

AB is perpendicular to AP if the dot product is zero,

-8 ( k - 5 ) -2 ( k - 1 ) + 0 ( k - 3 ) = 0

-8k + 40 -2k + 2 = 0

10k = 42

k = 42/10 = 4.2

#1

Vector is a good ceral, not a good math.

Dixi

#2