A line passes through two point $A (2, - 3, - 1)$ and $B (8, - 1, 2)$ . The coordinates of a point on this line at a distance of $14$ units from $A$ are

(14, 1, 5)

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(- 10, - 7, 7)

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(86, 25, 41)

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None of these

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Solution

The correct option is A $(14, 1, 5)$
Given points are $A (2, - 3, - 1)$ and $B (8, - 1, 2)$
Therefore direction ratio of $A B$ are $l = \frac{6}{7}, m = \frac{2}{7}, n = \frac{3}{7}$ or $l = \frac{- 6}{7}, m = \frac{- 2}{7}, n = \frac{- 3}{7}$
Hence, coordinates of a point $14$ unit from point $A$ is given as, $(2 + 14 l, - 3 + 14 m, - 1 + 14 n)$
$\Rightarrow (14, 1, 5)$ or $(- 10, - 7, - 7)$
Hence, option 'A' is correct.

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A line passes through two point A(2,−3,−1) and B(8,−1,2). The coordinates of a point on this line at a distance of 14 units from A are

A line passes through two point $A (2, - 3, - 1)$ and $B (8, - 1, 2)$ . The coordinates of a point on this line at a distance of $14$ units from $A$ are