Question

Let $\vec{a}=\alpha_1 \hat{i}+\alpha_2 \hat{j}+\alpha_3 \hat{k}, \vec{b}=\beta_1 \hat{i}+\beta_2 \hat{j}+\beta_3 \hat{k}$ and $\vec{c}=\gamma_1 \hat{i}+\gamma_2 \hat{j}+\gamma_3 \hat{k}$ and $|\vec{a}|=2 \sqrt{2}$ makes the angle $\pi / 3$ with the plane of $\overrightarrow{\mathrm{b}}$ and $\overrightarrow{\mathrm{c}}$ and angle between $\overrightarrow{\mathrm{b}} \& \overrightarrow{\mathrm{c}}$ is $\pi / 6$ then the value of $\left|\begin{array}{lll}\alpha_1 & \alpha_2 & \alpha_3 \ \beta_1 & \beta_2 & \beta_3 \ \gamma_1 & \gamma_2 & \gamma_3\end{array}ight|$ equals

Accepted Answer

$\left(\frac{\sqrt{3}(|\overrightarrow{\mathrm{b}}| \overrightarrow{\mathrm{c}} \mid)}{\sqrt{2}}\right)^{\mathrm{n}}$

Answer

$\left(\frac{|\vec{a} \| \vec{b}|}{2 	imes 3}ight)^n$

Answer

$\left(\frac{|\overrightarrow{\mathrm{c}} \| \overrightarrow{\mathrm{b}}|}{2 \sqrt{3}}\right)^{\mathrm{n} / 2}$

Answer

$\left(\frac{\sqrt{3}(|\overrightarrow{\mathrm{a}}||\overrightarrow{\mathrm{b}}|)}{\sqrt{2}}\right)^{\mathrm{n}}$

JEE MATHEMATICS MCQ: CROSS PRODUCT

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