A) \[\frac{1}{\sqrt{69}}\,(\mathbf{i}+2\mathbf{j}-8\mathbf{k})\]
B) \[\frac{1}{69}\,(\mathbf{i}+2\mathbf{j}-8\,\mathbf{k})\]
C) \[\frac{1}{\sqrt{69}}\,(-\mathbf{i}-2\mathbf{j}+8\mathbf{k})\]
D) \[\frac{1}{69}\,(-\mathbf{i}-2\mathbf{j}+8\,\mathbf{k})\]
Correct Answer: C
Solution :
Since \[\overrightarrow{AB}+\overrightarrow{BD}=\overrightarrow{AD}\Rightarrow \overrightarrow{BD}=\overrightarrow{AD}-\overrightarrow{AB}\] \[=(\mathbf{i}+2\mathbf{j}+3\mathbf{k})-(2\mathbf{i}+4\mathbf{j}-5\mathbf{k})=-\mathbf{i}-2\mathbf{j}+8\mathbf{k}\] Hence unit vector in the direction of \[\overrightarrow{BD}\] is \[\frac{-\mathbf{i}-2\mathbf{j}+8\mathbf{k}}{|-\mathbf{i}-2\mathbf{j}+8\mathbf{k}|}=\frac{-\mathbf{i}-2\mathbf{j}+8\mathbf{k}}{\sqrt{69}}.\]You need to login to perform this action.
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