Home
Class 12
MATHS
Using section formula, prove that the po...

Using section formula, prove that the points A(-2, 3, 5), B(1,2,3) and C(7,0, -1) are collinear.

Text Solution

Verified by Experts

Let the given points are collinear and B divides AC in the ratio K : 1.
Then the coordinates of B are
`((7k-2)/(k+1), 3/(k+1), (-k+5)/(k+1))`

But coordinates of B are (1, 2, 3)
So, `(7k-2)/(k+1)= 1, 3/(k+1)= 2 and (-k+5)/(k+1)= 3`
From each of these equations, we get
`k = 1/2`
Since, each of these equations give the same value of k. Therefore, the given points are collinear
and B divides AB internally in the ratio 1 : 2.
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    AAKASH INSTITUTE|Exercise Illustration|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    AAKASH INSTITUTE|Exercise TRY YOURSELF|97 Videos

  • STRAIGHT LINES

    AAKASH INSTITUTE|Exercise SECTION-J (AAKASH CHALLENGERS QUESTIONS)|5 Videos

  • TRIGNOMETRIC FUNCTIONS

    AAKASH INSTITUTE|Exercise Section - J (Akash Challengers Question)|15 Videos

Similar Questions

Explore conceptually related problems

(i) Using section formula, show that the points A(-2, 3,5), B(1,2,3) and C(7,0,-1) are collinear. (ii) Using division formula, prove that the points (2,3,4),(-1,-2,1) and (5,8,7) are collinear.

Using the section formula,prove that the three pints A(-2,3,5),B(1,2,3) and C(7,0,-1) are collinear.

Show that the points (-2,3,5),(1,2,3) and (7,0,-1) are collinear.

Prove that the point A(1,2,3), B(-2,3,5) and C(7,0,-1) are collinear.

Prove that the points A(2,0,-3), B (1,-2,-5) and C(3,2,-1) are collinear.

Using the distance formula, prove that the points A(-2,3), B(1,2) and C(7,0) are collinear.

Using section formula,show that the points A(2,-3,4),B(-1,2,1) and C(0,1/3,2) are collinear.

Show that the points A(1,2,7),B(2,6,3) and C(3,10,-1) are collinear.

Using section formula prove that the three points (-4,6,10),(2,4,6) and (14,0,-2) are collinear

Prove that the points A(3,-2,4) , B(3,-2,4), B(1,1,1) and C(-1,4,-2) are collinear.