Let a = i + j + k , b = i - j + k and c = i - j - k be three vectors. A vector v in the plane of a and b , whose projection on c is 1 3 , is given by

Step-by-step solution

a = i + j + k , b = i - j + k and c = i - j - k v is in the plane of a and b . aligned & v = m a +n ~b & v =(m+n) i +(m-n) j +(m+n) k ...(i) aligned Projection of v on c = v c | c | = 1 3 aligned & (m+n)(1)+(m-n)(-1)+(m+n)(-1) 1+1+1 = 1 3 & -m+n=1 & n =1+ m & v =(2 ~m +1) i - j +(2 ~m +1) k [ From (i) ] aligned When m =1 then v =3 i - j +3 k