Volume of purullclopipcd determined by vectors a + b, b + c and c… - Vidyadip

MCQ

Volume of purullclopipcd determined by vectors $\vec a + \vec b,\vec b + \vec c$ and $\vec c + \vec a$ is $4$. Then the volume of the parallelopiped determined by vectors $\vec a \times \vec b,\vec b \times \vec c$ and $\vec c \times \vec a$ is

A
$24$
B
$16$
C
$8$
✓
$4$

✓

Answer

Correct option: D.

$4$

d
$[\vec{a}+\vec{b} \quad \vec{b}+\vec{c} \quad \vec{c}+\vec{a}]=4 \Rightarrow[\vec{a} \vec{\,b} \vec{\,c}]=2$

New volume $=[\vec{a} \times \vec{b} \quad \vec{b} \times \vec{c} \quad \vec{c} \times \vec{a}]$

$=\left[\begin{array}{lll}{\vec{a}} & {\vec{b}} & {\vec{c}}\end{array}\right]^{2}=4$

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