Perpendicular vector

Question

a=2i+3j+5k point(2,7,5) find its perpendicular vector

Answer 1

Two vectors, a and b, are orthogonal or perpendicular if a•b=0.

Let b=(p,q,r)+(2,7,5) then we have b=(p+2)i+(q+7)j+(r+5)k.

a•b=2(p+2)+3(q+7)+5(r+5)=0. 2p+4+3q+21+5r+25=0, 2p+3q+5r+50=0.

The general equation of the perpendicular plane is 2x+3y+5z+50=0.