Vectors
Scalar triple product identity
MJMT_Full_Test_06
Grade 12
Question:
The scalar triple product $[\vec{a}+\vec{b}-\vec{c}\quad\vec{b}+\vec{c}-\vec{a}\quad\vec{c}+\vec{a}-\vec{b}]$ is equal to
0
$[\vec{a}\;\vec{b}\;\vec{c}]$
$2[\vec{a}\;\vec{b}\;\vec{c}]$
$4[\vec{a}\;\vec{b}\;\vec{c}]$
Step-by-Step Solution
Key Concept: Let $P=\vec{a}+\vec{b}-\vec{c}$, $Q=\vec{b}+\vec{c}-\vec{a}$, $R=\vec{c}+\vec{a}-\vec{b}$. Compute $Q\times R=2(\vec{b}\times\vec{c})+2(\vec{c}\times\vec{a})$. Then $P\cdot(Q\times R)=4[\vec{a}\;\vec{b}\;\vec{c}]$.
$4[\vec{a}\;\vec{b}\;\vec{c}]$.
Correct Answer: 4