JEE Mains · Maths · STD 12 - 11. three dimension geometry
Let a line \(L\) pass through the point \(P (2,3,1)\) and be parallel to the line \(x+3 y-2 z-2=0=x-y+2 z\). If the distance of \(L\) from the point \((5,3,8)\) is \(\alpha\), then \(3 \alpha^2\) is equal to \(......\).
- A \(157\)
- B \(158\)
- C \(159\)
- D \(156\)
Answer & Solution
Correct Answer
(B) \(158\)
Step-by-step Solution
Detailed explanation
\(\left|\begin{array}{ccc}\hat{ i } & \hat{ j } & \hat{ k } \\ 1 & 3 & -2 \\ 1 & -1 & 2\end{array}\right|=4 \hat{ i }-4 \hat{ j }-4 \hat{ k }\) \(\therefore\) Equation of line is \(\frac{ x -2}{1}=\frac{ y -3}{-1}=\frac{ z -1}{-1}\) Let \(Q\) be \((5,3,8)\) and foot of \(\perp\)…
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