Let a unit vector u = xi + yj + zk make angles π/2, π/3, 2π/3 with the vectors p₁ = 1/√2i + 1/√2k, p₂ = 1/√2j…

Question

Let a unit vector $$u = x\hat{i} + y\hat{j} + z\hat{k}$$ make angles $$\frac{\pi}{2}$$, $$\frac{\pi}{3}$$, $$\frac{2\pi}{3}$$ with the vectors $$p_1 = \frac{1}{\sqrt{2}}\hat{i} + \frac{1}{\sqrt{2}}\hat{k}$$, $$p_2 = \frac{1}{\sqrt{2}}\hat{j} + \frac{1}{\sqrt{2}}\hat{k}$$, and $$p_3 = \frac{1}{\sqrt{2}}\hat{i} + \frac{1}{\sqrt{2}}\hat{j}$$, respectively. If $$v = \frac{1}{\sqrt{2}}(\hat{i} + \hat{j} + \hat{k})$$, then $$|u - v|^2$$ is equal to:

Accepted Answer

B. $$\frac{5}{2}$$

Answer

A. $$\frac{11}{2}$$

Answer

C. $$9$$

Answer

D. $$7$$

Answer & step-by-step solution

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