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Section Formula

A line passes...

Question

A line passes through the points whose position vectors are $^i +^j - 2^k$ and $^i - 3^j +^k$ . The position vector of a point on it at unit distance from the first point is

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Solution

$\begin{matrix} A (1, 1, - 2) B (1, - 3, 1) E q u a t i o n o f l i n e t h r o u g h A a n d B \frac{x - 1}{0} = \frac{y - 1}{4} = \frac{z + 2}{- 3} P (1, 4 r + 1, - 3 r - 2) P A = 1 \sqrt{{(4 r)}^{2} + {(- 3 r)}^{2}} = 1 5 | r | = 1 r = \pm \frac{1}{5} r = \frac{1}{5}, P (1, \frac{9}{5}, - \frac{13}{5}) r = - \frac{1}{5}, P (1, \frac{1}{5}, - \frac{7}{5}) \end{matrix}$

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Q. A line passes through the points whose position vectors

^i +^j - 2^k

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