"Let Q be the mirror image of the point P(1, 0, 1) with respect to the plane S : x + y + z = 5. If a line L passing through (1, $-$1, $-$1), parallel to the line PQ meets the plane S at R, then QR2 is equal to :"

Question

Accepted Answer

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As L is parallel to PQ d.r.s of S is <1, 1, 1>

$\therefore$ $L \equiv {{x - 1} \over 1} = {{y + 1} \over 1} = {{z + 1} \over 1}$

Point of intersection of L and S be $\lambda$

$\Rightarrow (\lambda + 1) + (\lambda - 1) + (\lambda - 1) = S$

$\Rightarrow \lambda = 2$

$\therefore$ $R \equiv (3,1,1)$

Let $Q(\alpha ,\beta ,\gamma )$

$$ \Rightarrow {{\alpha - 1} \over 1} = {\beta \over 1} = {{\gamma - 1} \over 1} = {{ - 2( - 3)} \over 3}$$

$\Rightarrow \alpha = 3,\,\beta = 2,\,\gamma = 3$

$\Rightarrow Q \equiv (3,2,3)$

${(QR)^2} = {0^2} + {(1)^2} + {(2)^2} = 5$

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Let Q be the mirror image of the point P(1, 0, 1) with respect to the plane S : x + y + z = 5. If a line L passing through (1, $-$1, $-$1), parallel to the line PQ meets the plane S at R, then QR² is equal to :

Solution

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Let Q be the mirror image of the point P(1, 0, 1) with respect to the plane S : x + y + z = 5. If a line L passing through (1, $-$1, $-$1), parallel to the line PQ meets the plane S at R, then QR2 is equal to :

Solution

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More Three Dimensional Geometry questions

Drill 25 more like these. Every day. Free.

Let Q be the mirror image of the point P(1, 0, 1) with respect to the plane S : x + y + z = 5. If a line L passing through (1, $-$1, $-$1), parallel to the line PQ meets the plane S at R, then QR² is equal to :