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The vector equation of the plane which contains the point (1, 1, 8) and is normal to the line $r = 2 i + 3 j + 5 k + t (3 i - 2 j + 2 k)$ is

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$r \cdot (3 i - 2 j + 2 k) = 10$

$r . (2 i + 3 j + 5 k) = 45$

$r \cdot (3 i - 2 j + 2 k) = 17$

$r \cdot (2 i + 3 j + 5 k) = 10$

answer is B.

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Detailed Solution

$a = i + j + 8 k n = 3 i - 2 j + 2 k eq of plane r . n = a . n r . (3 i - 2 j + 2 k) = 3 - 2 + 16 r . (3 i - 2 j + 2 k) = 17$

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