A) \[\overset{\to }{\mathop{\alpha }}\,\]
B) \[3\overset{\to }{\mathop{\alpha }}\,\]
C) \[-\overset{\to }{\mathop{\alpha }}\,\]
D) \[\overset{\to }{\mathop{0}}\,\]
Correct Answer: A
Solution :
[a] Let \[\overrightarrow{\alpha }=\overrightarrow{a}\,\hat{i}+\overrightarrow{b}\hat{j}+\overrightarrow{c}\hat{k}\] Now, \[\overrightarrow{\alpha }\,\hat{i}=\left( \overrightarrow{a}\,\hat{i}+\overrightarrow{b}\,\hat{j}+\overrightarrow{c}\,\hat{k} \right).\hat{i}=\overrightarrow{a}\] \[\overrightarrow{\alpha }\,\hat{j}=\left( \overrightarrow{a}\,\hat{i}+\overrightarrow{b}\,\hat{j}+\overrightarrow{c}\,\hat{k} \right).\hat{j}=\overrightarrow{b}\] \[\overrightarrow{\alpha }\,\hat{k}=\left( \overrightarrow{a}\,\hat{i}+\overrightarrow{b}\,\hat{j}+\overrightarrow{c}\,\hat{k} \right).\hat{k}=\overrightarrow{c}\] Now, \[\overrightarrow{a}\,\hat{i}+\overrightarrow{b}\,\hat{j}+\overrightarrow{c}\,\hat{k}=\overrightarrow{\alpha }\] Thus, required expression = \[\overrightarrow{\alpha }\].
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