Home
Class 12
MATHS
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 .
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

  • DETERMINANTS

    CENGAGE|Exercise All Questions|268 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|7 Videos

Similar Questions

Explore conceptually related problems

let P an interioer point of a triangle A B C and A P ,B P ,C P meets the sides B C ,C A ,A BinD ,E ,F , respectively, Show that (A P)/(P D)=(A F)/(F B)+(A E)/(E C)dot

P is the variable point on the circle with center at CdotC A and C B are perpendiculars from C on the x- and the y-axis, respectively. Show that the locus of the centroid of triangle P A B is a circle with center at the centroid of triangle C A B and radius equal to the one-third of the radius of the given circle.

If P is a point on the altitude AD of the triangle ABC such the /_C B P=B/3, then AP is equal to 2asinC/3 (b) 2bsinC/3 2csinB/3 (d) 2csinC/3

ABC is a triangle and P any point on BC. if vec P Q is the sum of vec A P + vec P B + vec P C , show that ABPQ is a parallelogram and Q , therefore , is a fixed point.

If H is the orthocentre of triangle A B C ,R= circumradius and P=A H+B H+C H , then P=2(R+r) (b) maxof P is 3R minofP is 3R (d) P=2(R-r)

Points A, B, C lie on the parabola y^2=4ax The tangents to the parabola at A, B and C, taken in pair, intersect at points P, Q and R. Determine the ratio of the areas of the triangle ABC and triangle PQR

Let A B be chord of contact of the point (5,-5) w.r.t the circle x^2+y^2=5 . Then find the locus of the orthocentre of the triangle P A B , where P is any point moving on the circle.

If the angles A,B,C of a triangle are in A.P. and sides a,b,c, are in G.P., then prove that a^2, b^2,c^2 are in A.P.

Let ABC is be a fixed triangle and P be veriable point in the plane of triangle ABC. Suppose a,b,c are lengths of sides BC,CA,AB opposite to angles A,B,C, respectively. If a(PA)^(2) +b(PB)^(2)+c(PC)^(2) is minimum, then point P with respect to DeltaABC is

Statement 1: Let vec a , vec b , vec ca n d vec d be the position vectors of four points A ,B ,Ca n dD and 3 vec a-2 vec b+5 vec c-6 vec d=0. Then points A ,B ,C ,a n dD are coplanar. Statement 2: Three non-zero, linearly dependent coinitial vector ( vec P Q , vec P Ra n d vec P S) are coplanar. Then vec P Q=lambda vec P R+mu vec P S ,w h e r elambdaa n dmu are scalars.

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...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. G is the centroid of triangle A B Ca n dA1a n dB1 are rthe midpoint...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. If vec aa n d vec b are any two vectors of magnitudes 2 and 3, resp...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. The position vectors of the points P,Q,R,S are hati+hatj+hatk,2hati+5h...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |