Let a be a non-zero vector parallel to the line of intersection of the two planes described by i + j, i + k an…

Question

Let $$\mathbf{a}$$ be a non-zero vector parallel to the line of intersection of the two planes described by $$\hat{i} + \hat{j}$$, $$\hat{i} + \hat{k}$$ and $$\hat{i} - \hat{j}$$, $$\hat{i} - \hat{k}$$. If $$	heta$$ is the angle between the vector $$\mathbf{a}$$ and the vector $$\mathbf{b} = 2\hat{i} - 2\hat{j} + \hat{k}$$ and $$\mathbf{a} \cdot \mathbf{b} = 6$$, then the ordered pair $$\left( 	heta, |\mathbf{a} 	imes \mathbf{b}| ight)$$ is equal to:

Accepted Answer

D. $$\left( \frac{\pi}{4}, 6 \right)$$

Answer

A. $$\left( \frac{\pi}{3}, 6 \right)$$

Answer

B. $$\left( \frac{\pi}{4}, 3\sqrt{6} \right)$$

Answer

C. $$\left( \frac{\pi}{3}, 3\sqrt{6} \right)$$

Answer & step-by-step solution

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