If for $a0$, the feet of perpendiculars from the points $A$ $(a,-2 a, 3)$ and $B(0,4,5)$ on the plane $lx+m y+n z=0$ are points $C(0,-a,-1)$ and $D$ respectively, then the length of line segment $C D$ is equal to: [JEE Main 2021, 16 Mar (Shift 1)]

Question

If for $a>0$, the feet of perpendiculars from the points $A$ $(a,-2 a, 3)$ and $B(0,4,5)$ on the plane $lx+m y+n z=0$ are points $C(0,-a,-1)$ and $D$ respectively, then the length of line segment $C D$ is equal to: [JEE Main 2021, 16 Mar (Shift 1)]

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If for \(a>0\), the feet of perpendiculars from the points \(A\) \((a,-2 a, 3)\) and \(B(0,4,5)\) on the plane \(lx+m…

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If for \(a&gt;0\), the feet of perpendiculars from the points \(A\) \((a,-2 a, 3)\) and \(B(0,4,5)\) on the plane \(lx+m…

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If for \(a>0\), the feet of perpendiculars from the points \(A\) \((a,-2 a, 3)\) and \(B(0,4,5)\) on the plane \(lx+m…