SOLUTION: Given vectors: OP = <4,1,-6> OQ = <2,-7,5> OR = <3,-2,4> Find the scalar n in OP+nOQ that is perpendicular to OR. Thx!

Algebra ->  College  -> Linear Algebra -> SOLUTION: Given vectors: OP = <4,1,-6> OQ = <2,-7,5> OR = <3,-2,4> Find the scalar n in OP+nOQ that is perpendicular to OR. Thx!      Log On


   

Question 1075449: Given vectors:
OP = <4,1,-6>
OQ = <2,-7,5>
OR = <3,-2,4>
Find the scalar n in OP+nOQ that is perpendicular to OR.
Thx!
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Given vectors:
OP = <4,1,-6>
OQ = <2,-7,5>
OR = <3,-2,4>
Find the scalar n in OP+nOQ that is perpendicular to OR.

OP+nOQ = <4,1,-6> + n<2,-7,5> = <4,1,-6> + <2n,-7n,5n> =

<4+2n,1-7n,-6+5n>

Two vectors are perpendicular if and only if their scalar 
(dot)-product is 0, so we set the dot product (OP+nOQ)•OR = 0, 
or 

<4+2n,1-7n,-6+5n>•<3,-2,4> = 3(4+2n)-2(1-7n)+4(-6+5n) =

                                   12+6n-2+14n-24+20n = 0
                                              -14+40n = 0
                                                  40n = 14
                                                    n = 14/40
                                                    n = 7/20

Edwin