A) \[\hat{i}+\hat{j}+2\hat{k}\]
B) \[\hat{i}-\hat{j}+2\hat{k}\]
C) \[\hat{i}+\hat{j}-2\hat{k}\]
D) none
Correct Answer: A
Solution :
| A vector along the angle bisector = \[\hat{a}+\hat{b}\] |
| \[=\frac{(-4\hat{i}+3\hat{k})}{5}+\frac{(14\hat{i}+2\hat{j}-5\hat{k})}{15}\] |
| \[\frac{-12\hat{i}+9\hat{k}+14\hat{i}+2\hat{j}-5\hat{k}}{15}\] |
| \[=\frac{2(\hat{i}+\hat{j}+2\hat{k})}{15},\vec{d}=\sqrt{6}\left( \frac{\left( \hat{i}+\hat{j}+2\hat{k} \right)}{\sqrt{{{1}^{2}}+{{1}^{2}}+{{2}^{2}}}} \right)\]\[\therefore \,\,\,\,\,\,\,\vec{d}=\hat{i}+\hat{j}+2\hat{k}\] |
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