Vector Algebra Question 269
Question: If vectors $ \vec{a} $ and $ \vec{b} $ are two adjacent sides of a Parallelogram, then the vector representing the altitude of the parallelogram which is perpendicular to $ \vec{a} $ is
Options:
A) $ \vec{b}+\frac{\vec{b}\times \vec{a}}{{{| {\vec{a}} |}^{2}}} $
B) $ \frac{\vec{a}\cdot \vec{b}}{{{| {\vec{b}} |}^{2}}} $
C) $ \vec{b}-\frac{\vec{b}\cdot \vec{a}}{{{| {\vec{a}} |}^{2}}}\vec{a} $
D) $ \frac{\vec{a}\times (\vec{b}\times \vec{a})}{{{| {\vec{b}} |}^{2}}} $
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Answer:
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}}{{{| {\vec{a}} |}^{2}}} $
BETA
