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Let \(\vec{a}=\hat{i}+2\hat{j}+\hat{k}\) and \(\vec{b}=2\hat{i}+\hat{j}-\hat{k}\). Let \(\hat{c}\) be a unit vector in t…

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Let \(\vec{a}=\hat{i}+2\hat{j}+\hat{k}\) and \(\vec{b}=2\hat{i}+\hat{j}-\hat{k}\). Let \(\hat{c}\) be a unit vector in the plane of the vectors \(\vec{a}\) and \(\vec{b}\) and be perpendicular to \(\vec{a}\). Then such a vector \(\hat{c}\) is:

a

\(\frac{1}{\sqrt{5}}(\hat{j}-2\hat{k})\)

b

\(\frac{1}{\sqrt{3}}(-\hat{i}+\hat{j}-\hat{k})\)

c

\(\frac{1}{\sqrt{3}}(\hat{i}-\hat{j}+\hat{k})\)

d

\(\frac{1}{\sqrt{2}}(-\hat{\mathrm{i}}+\hat{\mathrm{k}})\)

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