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 of B are

• 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).