## Problem on the angle between vectors in 3d Sketch all 3d vectors whose angle with respect to the vector $\bfi$ is
1. $\pi/6$
2. $\pi/2$
3. $5\pi/6$
• ## Solution Recall that We consider vectors that share the origin as their base. #### Part (a) In any plane containing $\bfk$, the vectors that have an angle $\pi/6$ with respect to $\bfk$ are:   There are many planes containing $\bfk$, such as:   Putting together the vectors over all possible planes containing $\bfk$, we get that the vectors with angle $\pi/6$ from $\bfk$ form a cone:   #### Part (b) In any plane containing $\bfk$, the vectors that have an angle $\pi/2$ with respect to $\bfk$ are:   Considering all possible planes containing $\bfk$, the vectors with angle $\pi/2$ from $\bfk$ are a plane:   #### Part (c) In any plane containing $\bfk$, the vectors that have an angle $5\pi /6$ with respect to $\bfk$ are:   Considering all possible planes containing $\bfk$, the vectors with angle $5\pi/6$ from $\bfk$ are a cone that opens away from $\bfk$:  