Question

..........help please

Answer 1

Solution: Let the unit vector be ,P= Ai + Bj+Ck

i.e,

It is orthogonal to ,M= 3 i + 2 j + 6k.

So ,→ M.P=MP cos90°= 0

→3 A + 2 B + 6 C = 0  → [i × i=j×j=k×k=1,i×j=j×k=k×i=0]

And , P= Ai + Bj+Ck is coplanar with the vectors Q=2i+j+k and S= i.

So,→P.[Q×S]=0 or→S.[P×Q]=0

→

is equal to Zero.

Which gives ,C-B=0

So,the three equations are

→   ----(1)

→ B - C =0→B =C  ------(2)

→3 A + 2 B + 6 C= 0  ------(3)

Substituting B=C in (1) and (3),the equation (1)and (3) reduces to  

A²+2 C²= 1--------------(4)

3 A + 8 C =0

A = - 8 C/3

Equation (4) ,reduces to

→64 C²/9 + 2 C² =1

→ 82 C²=9

→ C² = 9/82

→ C = 3/√82=B

A = - 8 C/3= (- 8/3)×(3/√82)= -8/√82

So,the unit vector P is=Ai +Bj+Ck=   where i, j,k are unit vectors on coordinate axis.