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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 PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
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  2. A vector of magnitude sqrt(2) coplanar with the vector vec a= hat i+ ...

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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...

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  5. Points vec a , vec b , vec c ,a n d vec d are coplanar and (s inalpha...

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  6. If vec aa n d vec b are any two vectors of magnitudes 1 and 2, resp...

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  7. If vec a and vec b are any two vectors of magnitudes 2 and 3, respe...

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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 vec u , vec va n d vec w be such that | vec u|=1,| vec v|=2a n d|...

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  11. If veca, vecb and vecc be three non-coplanar vectors and a',b' and c' ...

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  12. if vecalpha||( vecbetaxx vecgamma) , then ( vecalphaxxbeta).(vecalpha...

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

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  14. Given three vectors vec a , vec b ,a n d vec c two of which are non-c...

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  15. If vec a and vec b are unit vectors such that ( vec a+ vec b).[(2 ve...

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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. vec a=2 hat i- hat j+ hat k , vec b= hat i+2 hat j- hat k , vec c= hat...

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  19. If P is any arbitrary point on the circumcircle of the equilateral t...

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  20. If vec ra n d vec s are non-zero constant vectors and the scalar b...

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