Question

Let \( \vec{a} = 2\hat{i} + \hat{j} - 2\hat{k} \) and \( \vec{b} = \hat{i} + \hat{j} \), if \( \vec{c} \) is a vector such that \( \vec{a} \cdot \vec{c} = |\vec{c}| \), \( |\vec{c} - \vec{a}| = 2\sqrt{2} \), and the angle between \( \vec{a} \times \vec{b} \) and \( \vec{c} \) is \( 30^\circ \), then \( |(\vec{a} \times \vec{b}) \times \vec{c}| \) is equal to

• A. $2/3$
• B. $3/2$
• C. 2
• D. 3

Hint:

Let $\veca=2\hati+\hatj-2\hatk$ and $\vecb=\hati+\hatj$, if $\vecc$ is a vector such that $\veca·\vecc=|\vecc|$, $|\vecc-\veca|=2\sqrt2$ and the angle between $\vecax\vecb$ and $\vecc$ is $30$, then $|(\vecax\vecb)x\vecc|$ is equal to

Answer 1

The Correct Option is B