Assuming v=4i−j+k and w=2i+3j−k.
Find a scalar s such that v is orthogonal to v— sw
Okay, so I know that two vectors are orthogonal when the dot product is 0. Or v • (v— sw) =0
What strategy would you use to solve this? I feel like this is probably a very simple question, but I am not sure where to begin.
$$\mathbf{v}\cdot(\mathbf{v}-s\mathbf{w})=0$$ $$|\mathbf{v}|^2-(\mathbf{v}.\mathbf{w})s=0$$ $$|\mathbf{v}|^2-(\mathbf{v}.\mathbf{w})s=0$$ $$s=\frac{|\mathbf{v}|^2}{(\mathbf{v}.\mathbf{w})}=\frac{16+1+1}{8-3-1}$$