jee-advanced 2013 Q60

jee-advanced · India · paper2 Vectors: Cross Product & Distances
Match List I with List II and select the correct answer using the code given below the lists:
List I
  • [P.] Volume of parallelepiped determined by vectors $\vec { a } , \vec { b }$ and $\vec { c }$ is 2. Then the volume of the parallelepiped determined by vectors $2 ( \vec { a } \times \vec { b } ) , 3 ( \vec { b } \times \vec { c } )$ and $( \vec { c } \times \vec { a } )$ is
  • [Q.] Volume of parallelepiped determined by vectors $\vec { a } , \vec { b }$ and $\vec { c }$ is 5. Then the volume of the parallelepiped determined by vectors $3 ( \vec { a } + \vec { b } ) , ( \vec { b } + \vec { c } )$ and $2 ( \vec { c } + \vec { a } )$ is
  • [R.] Area of a triangle with adjacent sides determined by vectors $\vec { a }$ and $\vec { b }$ is 20. Then the area of the triangle with adjacent sides determined by vectors $( 2 \vec { a } + 3 \vec { b } )$ and $( \vec { a } - \vec { b } )$ is
  • [S.] Area of a parallelogram with adjacent sides determined by vectors $\vec { a }$ and $\vec { b }$ is 30. Then the area of the parallelogram with adjacent sides determined by vectors $( \vec { a } + \vec { b } )$ and $\vec { a }$ is

List II
  1. $100$
  2. $30$
  3. (values as given in the list)

Codes:
PQRS
(A)4231
(B)2314
(C)3412
(D)1432
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.] Volume of parallelepiped determined by vectors $\vec { a } , \vec { b }$ and $\vec { c }$ is 2. Then the volume of the parallelepiped determined by vectors $2 ( \vec { a } \times \vec { b } ) , 3 ( \vec { b } \times \vec { c } )$ and $( \vec { c } \times \vec { a } )$ is
  \item[Q.] Volume of parallelepiped determined by vectors $\vec { a } , \vec { b }$ and $\vec { c }$ is 5. Then the volume of the parallelepiped determined by vectors $3 ( \vec { a } + \vec { b } ) , ( \vec { b } + \vec { c } )$ and $2 ( \vec { c } + \vec { a } )$ is
  \item[R.] Area of a triangle with adjacent sides determined by vectors $\vec { a }$ and $\vec { b }$ is 20. Then the area of the triangle with adjacent sides determined by vectors $( 2 \vec { a } + 3 \vec { b } )$ and $( \vec { a } - \vec { b } )$ is
  \item[S.] Area of a parallelogram with adjacent sides determined by vectors $\vec { a }$ and $\vec { b }$ is 30. Then the area of the parallelogram with adjacent sides determined by vectors $( \vec { a } + \vec { b } )$ and $\vec { a }$ is
\end{itemize}

\textbf{List II}
\begin{enumerate}
  \item $100$
  \item $30$
  \item (values as given in the list)
\end{enumerate}

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