If the line joining the points $A(2,3,-1)$ and $B(3,5,-3)$ is perpendicular to the line joining $C(1,2,3)$ and $D(3, y, 7)$, then $y=$

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Aicharya · Accepted Answer

$ \begin{aligned} & 	ext {Given, } A=(2,3-1) \ & \qquad B=(3,5-3) \ & 	ext { DR's of } \mathbf{A B}=(3-2,5-3,-3+1)=(1,2,-2) \ & 	ext { and } C=(1,2,3) \ & \qquad D=(3, y, 7) \end{aligned} $ $ 	herefore \mathrm{DR}^{\prime} \mathrm{s} 	ext { of } \mathbf{C D}=(3-1, y-2,7-3)=(2, y-2,4) $ Given, $\mathbf{A B} \perp \mathbf{C D}$ $ \begin{aligned} & \Rightarrow a_1 a_2+b_1 b_2+c_1 c_2=0 \ & \Rightarrow(1)(2)+2(y-2)+(-2)(4)=0 \ & \Rightarrow 2 y-10=0 \ & \Rightarrow y=5 \end{aligned} $ Hence, option (c) is correct

If the line joining the points $A(2,3,-1)$ and $B(3,5,-3)$ is perpendicular to the line joining $C(1,2,3)$…

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