Vectors & 3D Geometry
Volume of parallelopiped under linear transformation
MJMT_Full_Test_01
Grade 12
Question:
Volume of parallelopiped determined by vectors $\vec{a},\vec{b},\vec{c}$ is 5. Then volume determined by $3(\vec{a}+\vec{b})$, $(\vec{b}+\vec{c})$ and $2(\vec{c}+\vec{a})$ is
Step-by-Step Solution
Key Concept: $[3(\vec{a}+\vec{b}),\,\vec{b}+\vec{c},\,2(\vec{c}+\vec{a})]=6\cdot[(\vec{a}+\vec{b}),(\vec{b}+\vec{c}),(\vec{c}+\vec{a})]=6\cdot2[\vec{a},\vec{b},\vec{c}]$.
Volume $=60$.
Correct Answer: 60