Question

If $AB=21,B\equiv (-2,1,-8)$ and the direction cosines of $AB$ are $\frac{6}{7},\frac{2}{7},\frac{3}{7}$ then the coordinates of $A$ are

• A. $(-16,-7,-1)$
• B. $(-20,-5,17)$
• C. $(16,7,1)$
• D. $(20,5,17)$

Answer 1

The correct option is A $(-16,-7,-1)$

$\begin{array}{c}LetcoordinateofA\left(x,y,z\right)\\ B\left(-2,1,-8\right)given\\ \Rightarrow AB=\sqrt{(x+2^2+{\left(y-1\right)}^2{\left(z+8\right)}^2}\\ \Rightarrow directionofAB=\frac{\left(x+2\right)}{z_1},\frac{\left(y-1\right)}{z_1}.\frac{\left(z+8\right)}{z_1}\\ \frac{x+2}{z_1}=\frac{6}{7}\\ \therefore x=16\\ \frac{y-1}{z_1}=\frac{2}{7}\\ \therefore y=7and\frac{z+8}{z_1}=\frac{3}{7},z=1\\ Hence,coordinateof\left(16,7,1\right)\end{array}$