Home
Class 11
MATHS
If veca,vecb,vecc are position vectors o...

If `veca,vecb,vecc` are position vectors of the vertices A,B,C of a triangle ABC, show that the area of the triangle ABC is `(1)/(2) |vecaxxvecb+vecbxxvecc+veccxxveca|`. Also deduce the condition for collinearity of the points A,B and C.

Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA -I

    SURA PUBLICATION|Exercise EXERCISE 8.5|25 Videos
  • VECTOR ALGEBRA -I

    SURA PUBLICATION|Exercise ADDITIONAL PROBLEMS SECTION -A (1- MARK)|9 Videos
  • VECTOR ALGEBRA -I

    SURA PUBLICATION|Exercise EXERCISE 8.3|19 Videos
  • TWO DIMENSIONAL ANALYTICAL GEOMETRY

    SURA PUBLICATION|Exercise ADDITIONAL PROBLEMS - SECTION - D|3 Videos

Similar Questions

Explore conceptually related problems

A (veca), B (vecb) and C (vecc) are the vertices of triangle ABC and R(vecr) is any point in the plane of triangle ABC, then vecr, (veca xx vecb + vecb xx vecc + vecc xx veca ) is always equal to

If veca,vecb,vecc are the position vectors of three collinear points, then which of the following is true?

Prove that [vecaxxvecb,vecbxxvecc,veccxxveca]=[veca,vecb,vecc]^(2)

If veca, vecb and vecc are position vectors of A,B, and C respectively of DeltaABC and if|veca-vecb|=4,|vecb-vec(c)|=2, |vecc-veca|=3 , then the distance between the centroid and incenter of triangleABC is

If the vertices A,B, C of a triangle ABC are (1,2,3),(-1, 0,0), (0, 1,2), respectively, then find angle ABC .

Let a,b,c be the sides of a triangle ABC, a=2c,cos(A-C)+cos B=1. then the value of C is

Prove that [vecaxxvecb,vecbxxvecc,veccxxveca]=[veca,vecb,vecc]^(2) .

In any triangle ABC, prove that a cos A+b cos B +c cos C =(8 triangle^(2))/(abc) .

If A , B and C are interior angles of a triangle ABC, then show that tan ((A+B) /(2)) =cot ©/(2)