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Let \( \overrightarrow{\mathbf{a}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \overrightarrow{\mathbf{b}}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}} \) and \( \overrightarrow{\mathbf{c}}=\hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}} \) be three vectors. A vector \( \overrightarrow{\mathbf{v}} \) in the plane of \( \overrightarrow{\mathbf{a}} \) and \( \overrightarrow{\mathbf{b}} \),
P whose projection on \( \overrightarrow{\mathbf{c}} \) is \( \frac{1}{\sqrt{3}} \), is given by
(2011)
W
(a) \( \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+3 \hat{\mathbf{k}} \)
(b) \( -3 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}-\hat{\mathbf{k}} \)
(c) \( 3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+3 \hat{\mathbf{k}} \)
(d) \( \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-3 \hat{\mathbf{k}} \)
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