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The plane passing through the points (1, 2, 1), (2, 1, 2) and parallel to the line, 2x = 3y, z = 1 also passes through the point :

(1) (2, 0, –1)

(2) (0, 6, –2)

(3) (0, –6, 2)

(4) (–2, 0, 1)

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Ans. (4) (–2, 0, 1)

Sol. Plane passes through (2, 1, 2) is

a(x – 2) + b(y – 1) + (z – 2) = 0

it also passes through (1, 2, 1)

$\therefore$    – a + b – c = 0 $\implies$ a – b + c = 0    .......(1)

given line

${x\over3}={y\over2}={z-1\over0}$ is parallel to (1)

$\therefore$   3a + 2b + c0 = 0

$\implies{a\over0-2}={b\over3-0}={c\over2+3}$

$\implies{a\over2}={b\over-3}=-{c\over2+3}$

$\implies{a\over2}={b\over-3}={c\over-5}$

$\therefore$   plane is 2x – 4 – 3y + 3 – 5z + 10 = 0

$\implies$ 2x – 3y – 5z + 9 = 0

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Your Coordinate geometry is really good!!!

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