Maharashtra Board Solutions for Chapter: Vectors, Exercise 3: Exercise 5.3

Determine whether $\overline{a}$ and $\overline{b}$ are orthogonal, parallel or neither. $\overline{a}=-9\hat{i}+6\hat{j}+15\hat{k},\overline{b}=6\hat{i}-4\hat{j}-10\hat{k}$.

Determine whether $\overline{a}$ and $\overline{b}$ are orthogonal, parallel or neither. $\overline{a}=2\hat{i}+3\hat{j}-\hat{k},\overline{b}=5\hat{i}-2\hat{j}+4\hat{k}$

Determine whether $\overline{a}$ and $\overline{b}$ are orthogonal, parallel or neither. $\overline{a}=-\frac{3}{5}\hat{i}+\frac{1}{2}\hat{j}+\frac{1}{3}\hat{k},\overline{b}=5\hat{i}+4\hat{j}+3\hat{k}$

Determine whether $\overline{a}$ and $\overline{b}$ are orthogonal, parallel or neither. $\overline{a}=4\hat{i}-\hat{j}+6\hat{k},\overline{b}=5\hat{i}-2\hat{j}+4\hat{k}$

Find the angle $P$ of the triangle whose vertices are $P(0,-1,-2),Q(3,1,4)$ and $R(5,7,1)$.

If $\hat{p},\hat{q}$ and $\hat{r}$ are unit vectors, find $\hat{p}·\hat{q}$

If $\hat{p},\hat{q}$ and $\hat{r}$ are unit vectors, find $\hat{p}·\hat{r}$

If a vector has direction angles $45°$ and $60°$ find the third direction angle.