Given three vectors ( a =2 i - j + k , b = i +2 j - k ) and ( c = i + j -2 k ), a vector in the plane of ( b ) and ( c ) whose projection on ( a ) is of magnitude ( 2 3 ) is

Step-by-step solution

Given three vectors are ( aligned a & =2 i - j + k , b = i +2 j - k and c & = i + j -2 k aligned ) Now, let a vector in plane of ( b ) and ( c ) is ( aligned d & = b + c & =(1+ ) i +(2+ ) j -(1+2 ) k aligned ) ( ) Projection of vectord on a is (= 2 3 ) ( aligned & d a | a | = 2 3 & 2(1+ )-(2+ )-(1+2 ) 4+1+1 = 2 3 & 2+2 -2- -1-2 =2 & =-3 aligned ) So, required vector ( d =-2 i - j +5 k ) Hence, option (a) is correct.