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 (vec a+vec b+vec c)/(4) respectively, then the position vector of the orthocentre of this triangle, is :

Vector Algebra: Let ABC be a triangle whose circumcentre is at P . If the position… | JEE Main 2016

JEE Main 2016 (Online) 10th AprilQuestion 1

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 :

Vector Algebra

$-\left(\frac{\vec a+\vec b+\vec c}{2}\right)$$\vec a+\vec b+\vec c$$\frac{\vec a+\vec b+\vec c}{2}$✓ Correct answer$\vec 0$

Solution

Since $H=3G-2P$ with $G=\frac{\vec a+\vec b+\vec c}{3}$: $H=(\vec a+\vec b+\vec c)-\frac{\vec a+\vec b+\vec c}{2}=\frac{\vec a+\vec b+\vec c}{2}$.

Vector Algebra - JEE Mathematics question (JEE Main 2016 (Online) 10th April)

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