If A = i + j +3 k , B =- i + j +4 k and C =2 i -2 j -8 k , then the angle between the vectors P = A + B + C and Q =( A B ) is (in degree)

Step-by-step solution

The vectors are determined from the given components: A = i + j + 3 k B = - i + j + 4 k C = 2 i - 2 j - 8 k Vector sum P : P = A + B + C = (1 - 1 + 2) i + (1 + 1 - 2) j + (3 + 4 - 8) k = 2 i - k Cross product Q : Q = A B = i (4 - 3) - j (4 - (-3)) + k (1 - (-1)) = i - 7 j + 2 k Dot product: P Q = (2)(1) + (0)(-7) + (-1)(2) = 0 Since the dot product equals zero and both vectors are non-zero, = 0 | P || Q | = 0 Thus, the angle between P and Q is = 90^ .