Question

The direction cosines of a line segment AB are $\frac{-2}{\sqrt{17}},\frac{3}{\sqrt{17}},\frac{-2}{\sqrt{17}}$. If AB = $\sqrt{17}$ and the co-ordinates of A are (3, -6, 10), then the co-ordinates

• A. (1, -2, 4)
• B. (2, 5, 8)
• C. (-1, 3, -8)
• D. (1, - 3, 8)

Answer 1

The correct option is D

(1, - 3, 8)

$x=3\pm \left(\frac{-2}{\sqrt{17}}\right)\left(\sqrt{17}\right),y=-6\pm \left(\frac{3}{\sqrt{17}}\right)\left(\sqrt{17}\right)$
and $z=10\pm \left(\frac{-2}{\sqrt{17}}\right)\left(\sqrt{17}\right).$
Hence the required co-ordinates are (1,-3,8) or (5,-9,12).