A) \[2\sqrt{5}\hat{i}+2\sqrt{5}\hat{j}+\sqrt{5}\hat{k}\]
B) \[2\sqrt{5}\hat{i}-2\sqrt{5}\hat{j}+\sqrt{5}\hat{k}\]
C) \[\sqrt{5}\hat{i}+\sqrt{5}\hat{j}+\sqrt{5}\hat{k}\]
D) \[\sqrt{5}\hat{i}+2\sqrt{5}\hat{j}+\sqrt{5}\hat{k}\]
Correct Answer: B
Solution :
[b] If \[\vec{a}=2\hat{i}-2\hat{j}+\hat{k}\] and \[\vec{c}=-\hat{i}+2\hat{k}\] \[|\vec{c}|=\sqrt{{{(-1)}^{2}}+{{2}^{2}}}=\sqrt{1+4}=\sqrt{5}\] \[|\vec{c}|.\vec{a}=\sqrt{5}.(2\hat{i}-2\hat{j}+\hat{k})\] \[\therefore \,\,|\vec{c}|.\vec{a}=2\sqrt{5}\hat{i}-2\sqrt{5}\hat{j}+\sqrt{5}\hat{k}\]
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