Home
Class 12
MATHS
Show that the four points A ,B , Ca n...

Show that the four points `A ,B , Ca n dD` with position vectors ` vec a , vec b , vec c` and ` vec d` respectively are coplanar if and only if `3 vec a-2 vec b+ vec c-2 vec d=0.`

Text Solution

Verified by Experts

The correct Answer is:
`(5vec(p)+6vec(r ))/(11)` or `(2vec(q)+9vec(s))/(11)`.
Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    MODERN PUBLICATION|Exercise EXERCISE 10 (d) Long Answer Type Questions (I)|6 Videos

  • VECTOR ALGEBRA

    MODERN PUBLICATION|Exercise EXERCISE 10 (d) Long Answer Type Questions (II)|1 Videos

  • VECTOR ALGEBRA

    MODERN PUBLICATION|Exercise EXERCISE 10 (c ) Long Answer Type Questions (I)|12 Videos

  • THREE DIMENSIONAL GEOMETRY

    MODERN PUBLICATION|Exercise CHAPTER TEST 11|11 Videos

Similar Questions

Explore conceptually related problems

Show that the four points A,B,C and D with position vectors vec a,vec b,vec c and vec d respectively are coplanar if and only if 3vec a-2vec b+vec c-2vec d=0

Prove that the points A,B and C with position vectors vec a,vec b and vec c respectively are collinear if and only if vec a xxvec b+vec b xxvec c+vec c xxvec a=vec 0

Show that the points A,B,C with position vectors 2vec a+3vec b+5vec c,vec a+2vec b+3vec c and 7vec a-vec c respectively,are collinear.

The vectors vec a,vec b,vec c,vec d are coplanar then

Show that the point A,B,C with position vectors vec a-2vec b+3vec c,2vec a+3vec b-4vec c and -7vec b+10vec c are collinear.

Show that the found points A,B,C,D with position vectors vec a,vec b,vec c,vec d respectively such that 3vec a-2vec b+5vec c-6vec d=vec 0 ,are coplanar .Also,find the position vector of the point of intersection of the line segments AC and BD.

Show that the vectors vec a,vec b,vec c are coplanar if and only if vec a+vec b,vec b+vec c and vec c+vec a are coplanar.

Show that the points with position vectors vec a-2vec b+3vec c,-2vec a+3vec b-vec c and 4vec a-7vec b+7vec c are collinear.

A,B,C and D are four points in a plane with position vectors vec a,vec b,vec c and vec d, respectively,such that (vec a-vec d)*(vec b-vec c)=(vec b-vec d)*(vec c-vec a)=0 Then point D is the of triangle ABC

Show that the points with position vectors vec a-2vec b+3vec c,-2vec a+3vec b+2vec c and -8vec a+13vec b are collinear whatever be vec a,vec b,vec c .