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MathematicsSingle correct+2Question 50 of 60

JEE Advanced 2013 · Paper 1, Mathematics question 50

Let PR→=3i^+j^−2k^\overrightarrow{PR}=3\hat i+\hat j-2\hat k and SQ→=i^−3j^−4k^\overrightarrow{SQ}=\hat i-3\hat j-4\hat k determine diagonals of a parallelogram PQRSPQRS and PT→=i^+2j^+3k^\overrightarrow{PT}=\hat i+2\hat j+3\hat k be another vector. Then the volume of the parallelepiped determined by the vectors PT→\overrightarrow{PT}, PQ→\overrightarrow{PQ} and PS→\overrightarrow{PS} is

Choose one option
Answer and worked solution

Official answer: C

Sides from diagonals. PR→=a⃗+b⃗\overrightarrow{PR}=\vec a+\vec b and SQ→=a⃗−b⃗\overrightarrow{SQ}=\vec a-\vec b with a⃗=PQ→\vec a=\overrightarrow{PQ}, b⃗=PS→\vec b=\overrightarrow{PS}:
a⃗=(2,−1,−3),b⃗=(1,2,1).\vec a=(2,-1,-3),\qquad\vec b=(1,2,1).

Volume.
∣1232−1−3121∣=1(5)−2(5)+3(5)=10.\begin{vmatrix}1&2&3\\2&-1&-3\\1&2&1\end{vmatrix}=1(5)-2(5)+3(5)=10.

(C)

Topics:Scalar and vector triple productsVector operations
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