Q77 / 200 · Manipal (MET) 2012 · Mathematics
The value of $[\mathbf{a} \mathbf{a}+\mathbf{b} \mathbf{a}+\mathbf{b}+\mathbf{c}]$ is
- A$[\mathrm{abc}]^2$
- Correct answerB$[\mathbf{a b c}$]
- C$2[\mathbf{a b} \mathbf{c}]$
- D$3[\mathbf{a b c}]$
Solution
Now, $\left[\begin{array}{lll}\mathbf{a} & \mathbf{a}+\mathbf{b} & \mathbf{a}+\mathbf{b}+\mathbf{c}\end{array}\right]$
$\begin{aligned}
& =[\mathbf{a} \times(\mathbf{a}+\mathbf{b})] \cdot(\mathbf{a}+\mathbf{b}+\mathbf{c}) \\
& =(\mathbf{a} \times \mathbf{b}) \cdot(\mathbf{a}+\mathbf{b}+\mathbf{c})=(\mathbf{a} \times \mathbf{b}) \cdot \mathbf{c} \\
& =[\mathbf{a} \mathbf{b} \mathbf{c}]
\end{aligned}$
Hence, the correct answer is option: 'B'.