jee-advanced 2013 Q59

jee-advanced · India · paper2 Vectors: Lines & Planes Find Cartesian Equation of a Plane
Consider the lines $L _ { 1 } : \frac { x - 1 } { 2 } = \frac { y } { - 1 } = \frac { z + 3 } { 1 } , L _ { 2 } : \frac { x - 4 } { 1 } = \frac { y + 3 } { 1 } = \frac { z + 3 } { 2 }$ and the planes $P _ { 1 } : 7 x + y + 2 z = 3 , P _ { 2 } : 3 x + 5 y - 6 z = 4$. Let $a x + b y + c z = d$ be the equation of the plane passing through the point of intersection of lines $L _ { 1 }$ and $L _ { 2 }$, and perpendicular to planes $P _ { 1 }$ and $P _ { 2 }$.
Match List I with List II and select the correct answer using the code given below the lists:
List I
  • [P.] $a =$
  • [Q.] $b =$
  • [R.] $c =$
  • [S.] $d =$

List II
  1. $13$
  2. $-3$
  3. $1$
  4. $-2$

Codes:
PQRS
(A)3241
(B)1342
(C)3214
(D)2413
Consider the lines $L _ { 1 } : \frac { x - 1 } { 2 } = \frac { y } { - 1 } = \frac { z + 3 } { 1 } , L _ { 2 } : \frac { x - 4 } { 1 } = \frac { y + 3 } { 1 } = \frac { z + 3 } { 2 }$ and the planes $P _ { 1 } : 7 x + y + 2 z = 3 , P _ { 2 } : 3 x + 5 y - 6 z = 4$. Let $a x + b y + c z = d$ be the equation of the plane passing through the point of intersection of lines $L _ { 1 }$ and $L _ { 2 }$, and perpendicular to planes $P _ { 1 }$ and $P _ { 2 }$.

Match List I with List II and select the correct answer using the code given below the lists:

\textbf{List I}
\begin{itemize}
  \item[P.] $a =$
  \item[Q.] $b =$
  \item[R.] $c =$
  \item[S.] $d =$
\end{itemize}

\textbf{List II}
\begin{enumerate}
  \item $13$
  \item $-3$
  \item $1$
  \item $-2$
\end{enumerate}

\textbf{Codes:}
\begin{tabular}{ l l l l l }
 & P & Q & R & S \\
(A) & 3 & 2 & 4 & 1 \\
(B) & 1 & 3 & 4 & 2 \\
(C) & 3 & 2 & 1 & 4 \\
(D) & 2 & 4 & 1 & 3 \\
\end{tabular}