JEE Mains · Maths · STD 12 - 10. vector algebra
Let the vectors \(\vec{a}, \vec{b}, \vec{c}\) represent three coterminous edges of a parallelopiped of volume V. Then the volume of the parallelopiped, whose coterminous edges are represented by \(\vec{a}, \vec{b}+\vec{c}\) and \(\vec{a}+2 \vec{b}+3 \vec{c}\) is equal to \(..........\,V\)
- A \(3\)
- B \(6\)
- C \(1\)
- D \(2\)
Answer & Solution
Correct Answer
(C) \(1\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & {[\vec{a}, \vec{b}+\vec{c}, \vec{a}+2 \vec{b}+3 \vec{c}]} \\ & =\left|\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 1 \\ 1 & 2 & 3\end{array}\right|[\vec{a} \vec{b} \vec{c}]=1(3-2) V=V \\ & \end{aligned}\)
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