jee-main 2016 Q89

jee-main · India · 10apr Vectors 3D & Lines Section Division and Coordinate Computation

Let $ABC$ be a triangle whose circumcentre is at $P$. If the position vectors $A , B , C$ and $P$ are $\vec{a}, \vec{b}, \vec{c}$ and $\frac { \vec { a } + \vec { b } + \vec { c } } { 4 }$ respectively, then the position vector of the orthocentre of this triangle, is :
(1) $- \left( \frac { \vec { a } + \vec { b } + \vec { c } } { 2 } \right)$
(2) $\vec { a } + \vec { b } + \vec { c }$
(3) $\frac { ( \vec { a } + \vec { b } + \vec { c } ) } { 2 }$
(4) $\overrightarrow { 0 }$

Let $ABC$ be a triangle whose circumcentre is at $P$. If the position vectors $A , B , C$ and $P$ are $\vec{a}, \vec{b}, \vec{c}$ and $\frac { \vec { a } + \vec { b } + \vec { c } } { 4 }$ respectively, then the position vector of the orthocentre of this triangle, is :\\
(1) $- \left( \frac { \vec { a } + \vec { b } + \vec { c } } { 2 } \right)$\\
(2) $\vec { a } + \vec { b } + \vec { c }$\\
(3) $\frac { ( \vec { a } + \vec { b } + \vec { c } ) } { 2 }$\\
(4) $\overrightarrow { 0 }$

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