I am preparing for an interview and I came across these questions online. I am having a hard time with them. Could someone help me out? I don't want the actual solution. Just the steps or basic ideas would be helpful. Thanks in advance.
1. A vector v has coordinates (a,b,c) in a given reference frame. Rotate the vector around the x axis in a positive direction such that the vector v lies in the closest xz halfplane at the end of the rotation. Compute the rotation angle.
2. Suppose A and B are two planes. A contains the two vectors a1 and a2; B contains the two vectors b1 and b2.
Compute the angle between the planes A and B from as a function of the four vectors a1, a2 ,b1, b2
Let c be a vector in B which makes the smallest angle with the normal to A. Find a formula for c.
Compute a formula for the intersection of A and B