Vectors
Triple Product
MMTS_Full_Test_20
Grade 12
Question:
If the volume of a parallelepiped whose coterminous edges are $\vec{a}+\vec{b}$, $\vec{b}+\vec{c}$, $\vec{c}+\vec{a}$ is 24, then volume of parallelepiped with edges $\vec{a},\vec{b},\vec{c}$ is
Step-by-Step Solution
Key Concept: $(\vec{a}+\vec{b})\cdot[(\vec{b}+\vec{c})\times(\vec{c}+\vec{a})]=2[\vec{a}\vec{b}\vec{c}]$
$[\vec{a}+\vec{b},\vec{b}+\vec{c},\vec{c}+\vec{a}]=2[\vec{a},\vec{b},\vec{c}]$. So $2V=24\Rightarrow V=12$.
Correct Answer: 3