Question

The projection of the line joining the points $(3,4,5)$ and $(4,6,3)$ on the line joining the points $(-1,2,4)$ and $(1,0,5)$ is

• A. $\frac{4}{3}$
• B. $\frac{2}{3}$
• C. $\frac{1}{3}$
• D. $\frac{1}{2}$

Answer 1

The correct option is A $\frac{4}{3}$

Let $AB=(4-3)\hat{i}+(6-4)\hat{j}+(3-5)\hat{k}=\hat{i}+2\hat{j}-2\hat{k}$ and $PQ=(1+1)\hat{i}+(0-2)\hat{j}+(5-4)\hat{k}=2\hat{i}-2\hat{j}+\hat{k}$
Hence projection of $AB$ on $PQ$ is $=\left|\frac{AB\cdot PQ}{|AB||PQ|}\right|$

$=\left|\frac{1\left(2\right)+2(-2)-2\left(1\right)}{\sqrt{3}\sqrt{3}}\right|$

$=\frac{4}{3}$