MCQ
If $\left[\begin{array}{lll}\vec{a} \times \vec{b} & \vec{b} \times \vec{c} & \vec{c} \times a\end{array}\right]=\lambda[\vec{a} \vec{b} \vec{c}]^2$, then $\lambda$ is equal to
- A3
- B
- C1
- D2
$\begin{aligned} & \text {(c) : }\left[\begin{array}{lll}\vec{a} \times \vec{b} & \vec{b} \times \vec{c} & \vec{c} \times \vec{a}\end{array}\right] \\ & =(\vec{a} \times \vec{b})\{(\vec{b} \times \vec{c}) \times(\vec{c} \times \vec{a})\} \\ & =(\vec{a} \times \vec{b})\{(\vec{b} \times \vec{c} \cdot \vec{a}) \vec{c}-(\vec{b} \times \vec{c} \cdot \vec{c}) \vec{a}\} \\ & =(\vec{a} \times \vec{b})[\vec{a} \vec{b} \vec{c}] \vec{c}=[\vec{a} \vec{b} \vec{c}][\vec{a} \vec{b} \vec{c}]=[\vec{a} \vec{b} \vec{c}]^2 \\ & \therefore \quad \text { On comparison, } \lambda=1\end{aligned}$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
value of z = 4x + 5y is _______.
| X = x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
| P$(X = x)$ | 0.05 | 0.10 | 0.15 | 0.20 | 0.25 | 0.15 | 0.10 |