If a , b , c are three coplanar vectors such that | a |=1,| b |=2 , b c =8 , the angle between b and c is 45^ , then | a ( b c )|=

Step-by-step solution

Given vectors a , b , c are coplanar with | a | = 1 , | b | = 2 , b c = 8 , and the angle between b and c is 45^ . To determine c 's magnitude, apply the dot product definition: b c = | b | | c | . Substitute known values: 8 = 2 | c | 1 2 , leading to | c | = 4 2 . Since the vectors are coplanar, a lies in the plane formed by b and c , while b c is perpendicular to this plane. Thus, the angle between a and b c is 90^ . The magnitude of the cross product is evaluated as: | a ( b c )| = | a | | b c | 90^ = | b c | .