Home
Class 11
MATHS
Using distance formula prove that the fo...

Using distance formula prove that the following points are collinear: `A(4,-3,-1),\ B(5,-7,6)a n d\ C(3,1,-8)`

Text Solution

Verified by Experts

The correct Answer is:
N/a
`AB=sqrt((5-4)^(2)+(-7+3)^(2)+(6+1)^(2))`
`=sqrt(1+16+49)=sqrt(66) `units.
`BC=sqrt((3-5)^(2)+(1+7)^(2)+(-8-6)^(2))`
`=sqrt(4+64+196)`
`=sqrt(264)=2sqrt(66)` units
and `AC=sqrt((3-4)^(2)+(1+3)^(2)+(-8+1)^(2))`
`=sqrt(1+16+49)=sqrt(66)` units
Now, `AB+AC=sqrt(66)+sqrt(66)`
`=2sqrt(66)=BC`
`therefore` A,B and C are collinear.
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION OF THREE DIMENSIONAL GEOMETRY

    NAGEEN PRAKASHAN|Exercise Exercise 12 A|5 Videos

  • INTRODUCTION OF THREE DIMENSIONAL GEOMETRY

    NAGEEN PRAKASHAN|Exercise Exercise 12 B|18 Videos

  • CONIC SECTION

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|8 Videos

  • LIMITS AND DERIVATIVES

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|30 Videos

Similar Questions

Explore conceptually related problems

Using distance formula prove that the following points are collinear: A(4,-3,-1),B(5,-7,6) and C(3,1,-8)

Using distance formula prove that the following points are collinear: A(3,-5,1),B(-1,0,8) and C(7,-10,-6)

Using distance formula prove that the following points are collinear: P(0,7,-7),Q(1,4,-5) and R(-1,10,-9)

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

Using vector method,prove that the following points are collinear: A(-3,-2-5),B(1,2,3) and C(3,4,7)

Using section formula show that the points are collinear: (2,-1,3),(4,3,1),(3,1,2)

Using section formula show that the points are collinear: (-2,3,5),(1,2,3),(7,0,-1)

Using the distance formula, show that the given points are collinear. (i) (1, -1), (5, 2) and (9, 5) (ii) (6, 9), (0, 1) and (-6, -7) (iii) (-1, -1), (2, 3) and (8, 11) (iv) (-2, 5), (0, 1) and (2, -3).

Using distance formula, examine whether the sets of points are collinear : (3, 5), (1, 1), (-2, -5)

Using distance formula, examine whether the sets of points are collinear : (5, 1), (1, -1), (11,4)