These are linear algebra problems for an advanced engineering math class.

1. Find the angles in the triangle with these vertices:

[2, -1, 0] , [5, -4, 3] , and [1, -3, 2]

2. Determine the value a so that vectors

x = 2i + aj + k and y = 4i - 2j - 2k are perpendicular. Compute x(dotproduct)y to verify the result.

3. Compute the inner product of the following functions on the interval [-pi, pi] with n and m distinct positive integers:

a. <sin mx, sin nx>

b. <cos mx, cos nx>

c. <cos mx, sin nx>

d. <cos nx, cos nx>

e. <sin nx, cos nx>

Which functions are orthogonal?

Any help would be greatly appreciated. Thanks in advance.