Let a = i + 2 j - k , b = -3 i + 2 j + k , c = 2 i - j + k , and d = 2 i + j - 3 k . If a vector v satisfies the equations v a = b and v c = d , then the value of | v |^2 is equal to :

Step-by-step solution

From the property of the cross product, the vector v a is orthogonal to v . Since v a = b , it follows that v b = 0 . Similarly, from v c = d , it follows that v d = 0 . Because v is orthogonal to both b and d , it must be parallel to their cross product b d . Let us compute b d : b d = ( -3 i + 2 j + k ) ( 2 i + j - 3 k ) b d = i (-6 - 1) - j (9 - 2) + k (-3 - 4) = -7 i - 7 j - 7 k Since v is parallel to -7( i + j + k ) , we can assume v = ( i + j + k ) for some scalar . Substitute this form of v back into the fir