A) \[\vec{b}+\frac{\vec{b}\times \vec{a}}{{{\left| {\vec{a}} \right|}^{2}}}\]
B) \[\frac{\vec{a}\cdot \vec{b}}{{{\left| {\vec{b}} \right|}^{2}}}\]
C) \[\vec{b}-\frac{\vec{b}\cdot \vec{a}}{{{\left| {\vec{a}} \right|}^{2}}}\vec{a}\]
D) \[\frac{\vec{a}\times (\vec{b}\times \vec{a})}{{{\left| {\vec{b}} \right|}^{2}}}\]
Correct Answer: C
Solution :
[c] Let \[\overrightarrow{OD}=t\vec{a}\] \[\therefore \overrightarrow{OD}=\vec{b}-t\vec{a}\] Or \[(\vec{b}-t\vec{a}).\vec{a}=0\]\[(\therefore \overrightarrow{DB}\bot \overrightarrow{OA})\] Or \[t=\frac{\vec{b}\cdot \vec{a}}{{{\left| {\vec{a}} \right|}^{2}}}\]You need to login to perform this action.
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