Vector Algebra
Volume of Parallelepiped with New Edges
nta_pyq_2023_apr
Grade 12
Question:
Coterminous edges $\vec{a},\vec{b},\vec{c}$ form parallelepiped of volume $V$. Volume with edges $\vec{a},\vec{b}+\vec{c},\vec{a}+2\vec{b}+3\vec{c}$ is equal to
Step-by-Step Solution
Key Concept: $[\vec{a},\vec{b}+\vec{c},\vec{a}+2\vec{b}+3\vec{c}]=\det\begin{pmatrix}1&0&0\\0&1&1\\1&2&3\end{pmatrix}[\vec{a}\vec{b}\vec{c}]$.
New volume $=V$.
Correct Answer: 3