Let a =2 i + j - k and b = i +3 j -5 k be two vectors, and r be a vector along the vector 3 a -2 b such that | r |= 74 . If the direction of r is opposite to that of 3 a -2 b , then r =

Step-by-step solution

Given a =2 i + j - k , b = i +3 j -5 k Now, 3 a -2 b =3(2 i + j - k )-2( i +3 j -5 k )=4 i -3 j +7 k Since r along the vector 3 a -2 b So, r =x(3 a -2 b )=x(4 i -3 j +7 k ) Now, | r |= 74 16 x^2+9 x^2+49 x^2 = 74 74 x^2= 74 x= 1 since, r is the opposite direction of 3 a -2 b So x =-1 r =-4 i +3 j -7 k