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 a = i + 2 j - 2 k and b = i - j + k . The magnitude of a is | a | = 1^2 + 2^2 + (-2)^2 = 3 . Squaring the given equation | c - a | = 2 2 yields: | c |^2 + | a |^2 - 2 a c = 8 Substituting | a | = 3 and a c = | c | : | c |^2 + 9 - 2| c | = 8 | c |^2 - 2| c | + 1 = 0 (| c | - 1)^2 = 0 | c | = 1 Calculating the cross product a b : a b = ( i + 2 j - 2 k ) ( i - j + k ) = -3 j - 3 k The magnitude is | a b | = (-3)^2 + (-3)^2 = 3 2 . The angle between a b and c is 60^ . Using the definition of the cross product mag