A) 1
B) 3
C) 5
D) 2
Correct Answer: C
Solution :
\ n is perpendicular to \[\mathbf{a}\] and \[\mathbf{b}\] \[\mathbf{n}=\mathbf{a}\times \mathbf{b}\]; \[\mathbf{n}=\]\[\frac{\left| \begin{matrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 1 & -1 & 0 \\ 1 & 1 & 0 \\ \end{matrix} \right|}{\sqrt{2}\times \sqrt{2}}\] = \[\frac{2\mathbf{k}}{2}=\mathbf{k}\] \ \[|\mathbf{c}\ .\ \mathbf{n}|\ =\,|(\mathbf{i}+3\mathbf{j}+5\mathbf{k}).(\mathbf{k})|\,=\ |5|\,=5\].
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