Hello everyone,

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.

Problems:

1. A vectorvhas 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 vectorsa1anda2; B contains the two vectorsb1andb2.

Compute the angle between the planes A and B from as a function of the four vectorsa1,a2,b1,b2Let

cbe a vector in B which makes the smallest angle with the normal to A. Find a formula forc.

Compute a formula for the intersection of A and B