Question

A point on XOZ-plane divides the join of $(5,-3,-2)$ and $(1,2,-2)$ at

• A. $\left(\frac{13}{5},0,-2\right)$
• B. $\left(\frac{13}{5},0,2\right)$
• C. $(5,0,2)$
• D. $(5,0,-2)$

Answer 1

The correct option is A $\left(\frac{13}{5},0,-2\right)$

$\begin{array}{c}Thelinethroughthepoint\left(5,-3,-2\right)\\ and\left(1,2,-2\right)\\ \overrightarrow{r}=\hat{i}+2\hat{j}-2\hat{k}+\lambda \left(4\hat{i}-5\hat{j}\right)\\ \overrightarrow{r}=\left(1+4\lambda \right)\hat{i}+\left(2-5\lambda \right)\hat{j}-2\overrightarrow{k}\\ equationofXOZplane\\ y=0\\ \therefore 2-5\lambda =0\\ \therefore \lambda =\frac{2}{5}\\ \therefore \overrightarrow{r}=\frac{13}{5}\hat{i}-2\hat{k}\\ \therefore \left(\frac{13}{5},0,-2\right)\\ Hence,\\ optionAiscorrectanswer.\end{array}$