Let a = i +2 j -2 k and b = i - j + k . If c is a vector such that a c =| c | , | c - a |=2 2 and the angle between a b and c is 60^ , then |( a b ) c | is equal to

Step-by-step solution

Given vectors a = i +2 j -2 k and b = i - j + k . The magnitude a is | a |= 1²+2²+(-2)² =3 . The condition a c =| c | implies 3| c | = | c | , where is the angle between a and c . For non-zero c , this yields = 1 3 . The second condition | c - a |=2 2 leads to | c - a |²=8 . Using the vector identity, | c |² + | a |² - 2( a c ) = 8 . Substituting known values, | c |² + 9 - 2| c | = 8 , simplifying to (| c |-1)²=0 , so | c |=1 . The cross product a b = vmatrix i & j & k 1 & 2 & -2 1 & -1 & 1 vmatrix = -3 j - 3 k , w