JEE Main 2016MathematicsThree Dimensional GeometryMediumMCQ

JEE Main 2016 — Three Dimensional Geometry Question with Solution

JEE Main 2016 (10 Apr Online)

Question

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 : 

Choose an option

Show full solutionCorrect option: C
Correct answer
Ca→ + b→ + c→2

Step-by-step explanation

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

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About this question

This is a previous-year question from JEE Main 2016, covering the Three Dimensional Geometry chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.