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Equation of a Plane : General Form

The distance ...

Question

The distance of the point $3^i + 5^k$ from the line parallel to vector $6^i +^j - 2^k$ and passing through the point $8^i + 3^j +^k$

A

2

u n i t s

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B

3

u n i t s

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C

4

u n i t s

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D

5

u n i t s

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Solution

The correct option is B $3$ $u n i t s$
$\begin{matrix} \frac{x - 8}{6} = \frac{y - 3}{1} = \frac{z - 1}{- 2} D i r e c t i o n r a t i o o f A B = (6 r + 5, r + 3, - 2 r - 4) 6 (6 r + 5) + r + 3 + 2 (2 r + 4) = 0 41 r + 41 = 0 r = 1 B = (2, 2, 3) A B = \sqrt{1 + 4 + 4} = 3 H e n c e, t h e o p t i o n B i s t h e c o r r e c t a n s w e r . \end{matrix}$

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