Answer to Question #143781 in Linear Algebra for Alecza

Question

Dot Product and Orthogonal
Answer the following with complete solutions:
1.) Given the following vectors: u=(1,2,-4) and v=(2, 3, 5)
Find the angle between u and v and their unit vector/s

2.) Suppose that B=(2, 2, 1) and makes 30 degrees with A, and A*B=6. What is the magnitude of A?

3.) What is the angle between A and B if A*B=0?

4.) Find (u+v)*(2u-v) given that u*u=4, u*v=5 and v*v=10.

5.) Determine if u and v are orthogonal if u=(cos(theta), sin(theta), -1); v=(sin(theta), -cos(theta), 0).

Answer 1

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