If a = i + j +2 k and b =3 i +2 j - k , the magnitude of [( a +3 b ) (2 a - b )] is

Step-by-step solution

Given a = i + j + 2 k and b = 3 i + 2 j - k , we determine |( a + 3 b ) (2 a - b )| . The first vector sum is a + 3 b = (1 i + 1 j + 2 k ) + (9 i + 6 j - 3 k ) = 10 i + 7 j - k The second vector is 2 a - b = (2 i + 2 j + 4 k ) - (3 i + 2 j - k ) = - i + 5 k Taking their dot product: (10)(-1) + (7)(0) + (-1)(5) = -15 The magnitude of this scalar is |-15| = 15 Final answer: 15