Vector Algebra Question 109
Question: If $ \overset{\to }{\mathop{a}},=2\hat{i}-2\hat{j}+\hat{k} $ and $ \overset{\to }{\mathop{c}},=-\hat{i}+2\hat{k} $ then $ |\overset{\to }{\mathop{c}},|.\overset{\to }{\mathop{a}}, $ is equal to:
Options:
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} $
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Answer:
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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