find the value of S so that V+SW is perpendicular to W

Question

If V=2i+j+2k and w=i+j-k, find the value of S so that V+SW is perpendicular to W

Answer 1

Calculate the V+SW.

V+SW= (2i+j+2k)+S(i+j-k)

          =(2+S)i+(1+S)j+(2-S)k

V+SW is perpendicular to W means dot product is zero.

(V+SW).W=0

[(2+S)i+(1+S)j+(2-S)k].(i+j-k)=0

(2+S)*1+(1+S)*1+(2-S)*(-1)=0

2+S+1+S-2+S=0

3S+1=0

S=-1/3