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Equation of a Plane Parallel to a Given Plane

The plane x...

Question

The plane $x - y - z = 2$ is rotated through $90^{\circ}$ about its line of intersection with the plane $x + 2 y + z = 2$ . Then equation of this plane in new position is

5 x + 4 y + z - 10 = 0

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4 x + 5 y + 3 z = 0

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2 x + y + 2 z = 9

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3 x + 4 y - 5 z = 9

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Solution

The correct option is A $5 x + 4 y + z - 10 = 0$
$x - y - z = 2$ Rotated about $90^{0}$
$\Rightarrow a_{1} = 1, b_{1} = - 1, c_{1} = - 1$
$\Rightarrow a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2} = 0$
$\Rightarrow (1) (a_{2}) - b_{2} - c_{2} = a_{1} - b_{2} - c_{2} = 0$
OPTION : A $\to 5 - 4 - 1 = 0$
Correct
OPTION : B $\to 4 - 5 - 3 \neq 0$
Wrong
OPTION : C $\to 2 - 1 - 2 \neq 0$
Wrong
OPTION : D $\to 3 - 4 + 5 \neq 0$
Wrong
Hence the answer is $5 x + 4 y + z - 10 = 0.$

Suggest Corrections

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