Let A B C be a triangle whose circumcentre is at P . If the position vectors A ,   B ,   C and P…

Let ABC be a triangle whose circumcentre is at P. If the position vectors A, B, C and P are a→,b→,c→ and a→+b→+c→4 respectively, then the position vector of the orthocentre of this triangle, is : 
  1. -a→ + b→ + c→2
  2. a→ + b→ + c→
  3. a→ + b→ + c→2
  4. 0→

Solution

O is orthocentre and G is centroid and C is circumcentre. G divides OC in 2: 1 ratio.
Position vector of centriod G→=a→+b→+c→3
Position vector of circum center C→=a→+b→+c→4
Apply Section Formula,
G→=2C→+R→3

3G→=2C→+R→

R→=3G→-2C→=(a→+b→+c→)-2a→+b→+c→4

=a→+b→+c→2

Asked in: JEE Main 2016 (10 Apr Online)

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