Find the angle between the vectors A =2 i +4 j +4 k and B =4 i +2 j -4 k .

Step-by-step solution

Given, A =2 i +4 j +4 k and B =4 i +2 j -4 k Let be the angle between A and B . By using dot product, A B =A B , where, A and B are magnitudes of A and B respectively. Now, aligned & A= 2^2+4^2+4^2 =6 & B= 4^2+2^2+(-4)^2 =6 aligned Substituting the values, in dot product, we get aligned & (2 i +4 j +4 k ) (4 i +2 j -4 k )=(6)(6) & 8+8-16=36 & =0 & =90^ aligned