A) \[\overrightarrow{a}\text{ }=\text{2\hat{i}}+\text{\hat{j}+ \hat{k}},\text{ }\overrightarrow{\text{b}}=\text{\hat{i}}+\text{2\hat{j}}-\text{\hat{k}}\]
B) \[\overrightarrow{c}\]
C) \[\overrightarrow{c}\]
D) 0
Correct Answer: C
Solution :
\[\underset{x\to 1}{\mathop{\lim }}\,(1-x)\tan \left( \frac{\pi x}{2} \right)\] put, \[1-x=y\] as\[x\to 1,y\to 0\] thus, \[\underset{y\to 0}{\mathop{\lim }}\,y\tan \frac{\pi (1-y)}{2}\] \[=\underset{y\to 0}{\mathop{\lim }}\,y\tan \frac{\pi (1-y)}{2}\] \[=\underset{y\to 0}{\mathop{\lim }}\,\frac{2}{\pi }\frac{\left( \frac{\pi y}{2} \right)}{\tan \left( \frac{\pi y}{2} \right)}\] \[=\frac{2}{\pi }\times 1\] \[=\frac{2}{\pi }\]
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