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.