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Vector Multiplication Problems 1. Find the angles between all three pairs of the vectors A = 3i + 2j, B = -i + 6j and C = 7i – 2j. 2. Given two vectors A = -2i + 3j + 4k and B = 3i + j - 3k, do the following. a) Find the magnitude of each vector. b) Write an expression for the vector difference A – B, using unit vectors. c) Find the magnitude of the vector difference A – B. Is this the same as the magnitude of B – A? Explain. 3. Obtain a unit vector perpendicular to the two vectors given in problem #2. 4. Find the cross product of the vectors A = i – 2j + 3k and B = 2i + 4j + 2k. 5. You are given vectors A = 5i – 6.5j and B = -3.5i + 7j. A third vector C lies in the xy-plane. Vector C is perpendicular to vector A, and the scalar product of C with B is 15. From this information, find the components of vector C. 6. Two vectors A and B have magnitude A = 3 and B = 3. Their vector product is A x B = -5k + 2i. What is the angle between A and B?