Vector-Algebra Question 401
Question: If $ \vec{a},\vec{b},\vec{c},\vec{d} $ are the position vectors of points A, B, C and D respectively such that $ (\vec{a}-\vec{d}).(\vec{b}-\vec{c})=(\vec{b}-\vec{d}).(\vec{c}-\vec{a})=0 $ then D is the
Options:
A) Centroid of $ \Delta ABC $
B) Circumcentre of $ \Delta ,ABC $
C) Orthocentre of $ \Delta ,ABC $
D) None of these
Correct Answer: C
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Answer:
Solution:
$ \therefore ,(\overset{\to }{\mathop{a}},-\overset{\to }{\mathop{d}},)(\overset{\to }{\mathop{b}},-\overset{\to }{\mathop{c}},)=0 $
$ \Rightarrow \overrightarrow{DA} $ and $ \overrightarrow{CB} $ are perpendicular $ (\overset{\to }{\mathop{b}},-\overset{\to }{\mathop{d}},)\cdot (\overset{\to }{\mathop{c}},-\overset{\to }{\mathop{a}},)=0 $
$ \Rightarrow \overrightarrow{DB} $ and $ \overrightarrow{AC} $ are perpendicular
$ \therefore $ D is orthocenter of $ \Delta ABC $
BETA
