If the plane $2x + y - 5z = 0$ is rotated about its line of intersection with the plane $3x - y + 4z - 7 = 0$ by an angle of ${\pi \over 2}$, then the plane after the rotation passes through the point :
Solution
<p>${P_1}:2x + y - 52 = 0$, ${P_2}:3x - y + 4z - 7 = 0$</p>
<p>Family of planes P<sub>1</sub> and P<sub>2</sub></p>
<p>$P:{P_1} + \lambda {P_2}$</p>
<p>$\therefore$ $P:(2 + 3\lambda )x + (1 - \lambda )y + ( - 5 + 4\lambda )z - 7\lambda = 0$</p>
<p>$\because$ $P \bot {P_1}$</p>
<p>$\therefore$ $4 + 6\lambda + 1 - \lambda + 25 - 20\lambda = 0$</p>
<p>$\lambda = 2$</p>
<p>$\therefore$ $P:8x - y + 32 - 14 = 0$</p>
<p>It passes through the point (1, 0, 2)</p>
About this question
Subject: Mathematics · Chapter: Three Dimensional Geometry · Topic: Direction Cosines and Ratios
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