Let a =2 i -3 j -5 k and b =3 i +2 j -5 k be two vectors and r be a vector in the plane of a and b . If r is orthogonal to the vector 5 i -2 j +3 k and the magnitude of r is 94 , then | r b |=

Step-by-step solution

Let c = a b = | array ccc i & j & k 2 & -3 & -5 3 & 2 & -5 array |=25 i -5 j +13 k Since, r lies on plane containing a and b therefore r is perpendicular to c and given that r is also perpendicular to vector 5 i -2 j +3 k aligned & r = | array ccc i & j & k 25 & -5 & 13 5 & -2 & 3 array |= [11 i -10 j -25 k ] and | r |= 94 & r = 1 3 (11 i -10 j -25 k ) aligned Now, | r , b |= 1 3 (33-20+125)=46 .