a = i + j + k , b =2 i + j + k are two vectors and c is a unit vector lying in the plane of a and b . If c is perpendicular b . then c ( i + j +2 k )=

Step-by-step solution

Vector lying in the plane of a & b is aligned & c = ( i - j + k )+ (2 i + j + k ) & c =( +2 ) i +( - ) j +( + ) k & c . b =2( +2 )+ - + + =0 & =6 +2 =0 aligned aligned & =-3 & c =- i +4 j -2 k ;| c |=1= ^2+4 ^2+16 ^2 & 1= 21 = 1 21 ; c = -1 21 i + 4 21 j - 2 21 k & c .( i + j +2 k )= 1 21 aligned