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Q.

If A = (1, 3, –5), B = (3, 5, –3) then the vector equation of the plane passing through the midpoint of AB and perpendicular to AB is

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a

$r . (i + j + k) = 2$

b

$r . (i + j + k) = 4$

c

$r . (i + j + k) = 3$

d

$r . (i + j + k) = 1$

answer is B.

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Detailed Solution

$a = midpoint AB = (2, 4, - 4) AB = n = (2, 2, 2) = (1, 1, 1) ∴ eq of plane r . n = a . n r . (i + j + k) = 2 + 4 - 4 = 2$

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