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  4. The unit vector parallel to resultant of the vectors A→ =4 widehati+3 widehatj+6 widehatk and B→ =- widehati+6 widehatj-8 widehatk is:

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Q. The unit vector parallel to resultant of the vectors $ A\to =4\widehat{i}+3\widehat{j}+6\widehat{k} $ and $ B\to =-\widehat{i}+6\widehat{j}-8\widehat{k} $ is:

EAMCETEAMCET 2000

Solution:

Resultant of $ \text{\vec{A}} $ and $ \text{\vec{B}} $ is $ \text{\vec{R}}\,\text{= \vec{A}}\,\text{+ \vec{B}} $ $ (4\hat{i}+3\hat{j}+6\hat{k})+(-\hat{i}+3\hat{j}-8\hat{k}) $ $ =3\hat{i}+6\hat{j}-2\hat{k} $ and $ |\vec{R}|=\sqrt{({{3}^{2}})+{{(6)}^{2}}+({{2}^{2}})} $ $ =\sqrt{9+36+4} $ $ =\sqrt{49}=7 $ Hence, unit vector along resultant $ \hat{n}=\frac{{\vec{R}}}{|\vec{R}|}=\frac{1}{7}(3\hat{i}+6\hat{j}-2\hat{k}) $