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Let P be a point interior to the acut...

Let `P` be a point interior to the acute triangle `A B Cdot` If `P A+P B+P C` is a null vector, then w.r.t traingel `A B C ,` point `P` is its a. centroid b. orthocentre c. incentre d. circumcentre

A

centroid

B

orthocentre

C

incentre

D

circumcentre

Text Solution

Verified by Experts

The correct Answer is:
a
`veca - vecp + vecb - vecp + vecc -vecp =0`
`or vecp = (veca + vecb + vecc)/3`
Hence, P is centroid .
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. Let the position vectors of the points Pa n dQ be 4 hat i+ hat j+la...

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  2. A vector of magnitude sqrt2 coplanar with the vectors veca=hati+hatj+2...

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  3. Let P be a point interior to the acute triangle A B Cdot If P A+P B...

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  4. G is the centroid of triangle ABC and A1 and B1 are the midpoints of s...

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  5. Points veca , vecb vecc and vecd are coplanar and (sin alpha)veca + (2...

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  6. If veca and vecb are any two vectors of magnitudes 1and 2. respectivel...

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  7. If veca and vecb are any two vectors of magnitude 2 and 3 respective...

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  8. veca, vecb and vecc are unit vecrtors such that |veca + vecb+ 3vecc|=4...

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  9. If the vector product of a constant vector vec O A with a variable...

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  10. Let vecu, vecv and vecw be such that |vecu|=1,|vecv|=2 and |vecw|=3 if...

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  11. If the two adjacent sides of two rectangles are reprresented by vector...

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  12. If vecalpha||(vecbxxvecgamma), then (vecalphaxxvecbeta).(vecalphaxxvec...

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  13. The position vectors of points A,B and C are hati+hatj,hati + 5hatj -h...

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  14. Given three vectors eveca, vecb and vecc two of which are non-collinea...

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  15. If veca and vecb are unit vectors such that (veca +vecb). (2veca + 3ve...

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  16. If in a right-angled triangle A B C , the hypotenuse A B=p ,t h e n...

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  17. Resolved part of vector veca and along vector vecb " is " veca1 and th...

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  18. Let veca=2hati=hatj+hatk, vecb=hati+2hatj-hatk and vecc=hati+hatj-2hat...

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  19. If P is any arbitrary point on the circumcirlce of the equllateral ...

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  20. If vecr and vecs are non-zero constant vectors and the scalar b is cho...

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