Assessment: Vectors in Three Dimensions

Find the magnitude of v=(6,8,0).

Find the dot product of a=(1,1,1) and b=(2,3,4).

Find the angle (in degrees) between a=(1,0,0) and b=(0,5,0).

Find the y-component of a×b for a=(0,1,0) and b=(0,0,1).

Find the area of the parallelogram formed by a=(4,0,0) and b=(0,6,0).

For the line r=(3+t, 1−2t, 5+t), find the z-coordinate at t=4.

A game engine needs a compact test for whether a point lies on a flat surface, given the surface's normal vector and one known point on it. Which equation gives this directly?

An engineer needs the volume of a parallelepiped-shaped storage tank, described by three edge vectors from one corner. Which technique gives this directly?

If a and b are perpendicular unit vectors, what is a·b?

Find the x-component of a×b for a=(0,2,0) and b=(0,0,3).