Let \( \mathrm{a}, \mathrm{b} \) and \( \mathrm{c} \) be distinct p...

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Let \( \mathrm{a}, \mathrm{b} \) and \( \mathrm{c} \) be distinct positive numbers. If the
\( \mathrm{P} \) vectors \( a \hat{i}+a \hat{j}+c \hat{k}, \hat{i}+\hat{k} \) and \( \hat{i}+\hat{c j}+b \hat{k} \) are co-

W planar, then \( \mathrm{c} \) is equal to:
(1) \( \frac{2}{\frac{1}{a}+\frac{1}{b}} \)
(2) \( \frac{a+b}{2} \)
(3) \( \frac{1}{\mathrm{a}}+\frac{1}{\mathrm{~b}} \)
(4) \( \sqrt{\mathrm{ab}} \)
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