A) \[\frac{1}{3}(3\hat{i}-6\hat{j}-2\hat{k})\]
B) \[\frac{1}{3}(3\hat{i}+6\hat{j}+2\hat{k})\]
C) \[\frac{1}{3}(3\hat{i}-6\hat{j}-3\hat{k})\]
D) \[\frac{1}{7}(3\hat{i}+6\hat{j}-2\hat{k})\]
E) \[\frac{1}{7}(3\hat{i}+5\hat{j}-3\hat{k})\]
Correct Answer: D
Solution :
Let \[{{\overrightarrow{R}}_{1}}=2\hat{i}+4\hat{j}-5\hat{k}\] and \[{{\overrightarrow{R}}_{2}}=\hat{i}+2\hat{j}+3\hat{k}\] \[\therefore \]\[\overrightarrow{R}\](along \[\overset{\to }{\mathop{AC}}\,\]) \[={{\overrightarrow{R}}_{1}}+{{\overrightarrow{R}}_{2}}\] \[=3\hat{i}+6\hat{j}-2\hat{k}\] \[\therefore \] \[\overrightarrow{a}\] (unit vector along\[\overset{\to }{\mathop{AC}}\,\])\[=\frac{\overset{\to }{\mathop{R}}\,}{|\overset{\to }{\mathop{R}}\,|}\] \[=\frac{3i+6\hat{j}-2\hat{k}}{\sqrt{9+36+4}}\] \[=\frac{1}{7}(3\hat{i}+6\hat{j}-2\hat{k})\]You need to login to perform this action.
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