Question

The direction ratios of $\overline{AB}$ are $-2,2,1$. If $A\equiv (4,1,5)$ and $l\left(AB\right)=6$ units, find the coordinates of $B$.

Answer 1

Given

$A(4,1,5)$

Drs of $AB$ is $(-2,2,1)$

Equation of line ${}^{\prime }A{B}^{\prime }$ is given by

$\frac{x-4}{-2}=\frac{y-1}{2}=\frac{z-5}{1}$

Let $B(-2\lambda +4,2\lambda +1,\lambda +5)$

Given

$AB=6$

$\Rightarrow A{B}^2=36$

$\Rightarrow (-2\lambda {)}^2+(-2\lambda {)}^2+(-\lambda {)}^2=36$

$\Rightarrow 9{\lambda }^2=36$

$\therefore \lambda =\pm \frac{6}{3}$

$\therefore \lambda =\pm 2$

$\therefore B(0,5,7)$

or

$B(8,-3,3)$