Home
Class 11
MATHS
Prove that the points (a ,b+c),(b ,c+a)a...

Prove that the points `(a ,b+c),(b ,c+a)a n d(c ,a+b)` are collinear.

Text Solution

AI Generated Solution

To prove that the points \( (a, b+c) \), \( (b, c+a) \), and \( (c, a+b) \) are collinear, we will calculate the slopes between pairs of points and show that they are equal. ### Step 1: Define the points Let: - Point A = \( (a, b+c) \) - Point B = \( (b, c+a) \) - Point C = \( (c, a+b) \) ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • BINOMIAL THEOREM

    RD SHARMA|Exercise Solved Examples And Exercises|228 Videos

  • COMBINATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|117 Videos

Similar Questions

Explore conceptually related problems

Prove that the points (a+b+c),(b,c+a) and (c,a+b) are collinear.

Prove that the points (a, b + c), (b, c + a) and (c, a + b) are collinear.

Knowledge Check

  • If the points (a,b),(c,d) and (a-c,b-d) are collinear, then

    A
    `ab=cd`
    B
    `ac=bd`
    C
    `ad=bc`
    D
    None

  • If the points A(1,2) , B(0,0) and C (a,b) are collinear , then

    A
    a=b
    B
    a=2b
    C
    2a=b
    D
    a=-b

    • Similar Questions

    Explore conceptually related problems

    Prove that the points (a, b), (c, d) and (a-c, b-d) are collinear, if ad = bc.

    Prove that the points A(a, 0), B(0, b) and C(1, 1) are collinear, if (1)/(a) + (1)/(b) = 1.

    Show that points A(a,b+c),B(b,c+a)C(c,a+b) are collinear.

    Prove that the (a, b+c), (b, c+a) and (c, a+b) are collinear.

    If a!=b!=c, prove that the points (a,a^(2)),(b,b^(2)),(c,c^(2)) can never be collinear.

    If the position vectors of the points A,B and C be a,b and 3a-2b respectively, then prove that the points A,B and C are collinear.

    Home
    Profile