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A line passing through the point $A (3 i + j + k)$ and parallel to $2 i - j + 2 k$ . If P is a point such that AP=15 then $OP$ is

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$(3 i + j + k) \pm 5 (2 i - j + 2 k)$

$(3 i + j - k) \pm 5 (2 i - j - 2 k)$

answer is B.

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Detailed Solution

$AP = t (2 i - j + 2 k) \Rightarrow |AP| = |t| \sqrt{4 + 1 + 4} 15 = |t| 3 \Rightarrow t = \pm 5 r = (3 i + j + k) \pm 5 (2 i - j + 2 k)$

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