Vectors — Maths STD 12 Science — Question

Then $\bar{a}=-\hat{i}+6 \hat{j}+5 \hat{k}, \bar{p}=\frac{-14 \hat{i}+39 \hat{j}+28 \hat{k}}{5}$

Now, $\mathrm{P}$ divides $\mathrm{AB}$ internally in the ratio $3: 2$

$\therefore \bar{p}=\frac{3 \bar{b}+2 \bar{a}}{5}$

$\therefore 5 \bar{p}=3 \bar{b}+2 \bar{a} \quad \therefore 3 \bar{b}=5 \bar{p}-2 \bar{a}$

$\therefore 3 \vec{b}=5\left(\frac{-14 \hat{i}+39 \hat{j}+28 \hat{k}}{5}\right)-2(-\hat{i}+6 \hat{j}+5 \hat{k})$

$\begin{aligned} & =-14 \hat{i}+39 \hat{j}+28 \hat{k}+2 \hat{i}-12 \hat{j}-10 \hat{k} \\ & =-12 \hat{i}+27 \hat{i}+18 \hat{k}\end{aligned}$

$\therefore \bar{b}=-4 \hat{i}+9 \hat{j}+6 \hat{k}$

∴ coordinates of B are (-4, 9, 6).