Let a be a unit vector perpendicular to the vectors b = i - 2j + 3k and c = 2i + 3j - k, and makes an angle of…

Question

Let $$\hat{a}$$ be a unit vector perpendicular to the vectors $$\mathbf{b} = \hat{i} - 2\hat{j} + 3\hat{k} \quad 	ext{and} \quad \mathbf{c} = 2\hat{i} + 3\hat{j} - \hat{k},$$ and makes an angle of $$\cos^{-1}\left( -\frac{1}{3} ight)$$ with the vector $$\hat{i} + \hat{j} + \hat{k}$$.
If $$\hat{a}$$ makes an angle of $$\frac{\pi}{3}$$ with the vector $$\hat{i} + \alpha \hat{j} + \hat{k}$$, then the value of $$\alpha$$ is:

Accepted Answer

C. $$-\sqrt{6}$$

Answer

A. $$-\sqrt{3}$$

Answer

B. $$\sqrt{6}$$

Answer

D. $$\sqrt{3}$$

Answer & step-by-step solution

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