Let a=5 i- j-3 k and b= i-3 j+5 k.

Question

Let $\vec a=5\hat i-\hat j-3\hat k$ and $\vec b=\hat i-3\hat j+5\hat k$. Which statement is TRUE?

Accepted Answer

$$\vec a\cdot\vec b = 5-3-15=-13,\qquad |\vec b|=\sqrt{1+9+25}=\sqrt{35}$$

$$\text{Projection} = \frac{\vec a\cdot\vec b}{|\vec b|} = -\frac{13}{\sqrt{35}}$$

Since the projection is negative, the projection vector points opposite to $\vec b$.

Solutions · 1