Home
Class 12
MATHS
Statement 1: if three points P ,Qa n ...

Statement 1: if three points `P ,Qa n dR` have position vectors ` vec a , vec b ,a n d vec c` , respectively, and `2 vec a+3 vec b-5 vec c=0,` then the points `P ,Q ,a n dR` must be collinear. Statement 2: If for three points `A ,B ,a n dC , vec A B=lambda vec A C ,` then points `A ,B ,a n dC` must be collinear.

A

Both the statements are true, and Statement 2 is the correct explanation for Statement 1.

B

Both the statements are true, but Statement 2 is not the correct explanation for Statement 1.

C

Statement 1 is true and Statement 2 is false.

D

Statement 1 is false and Statement 2 is true.

Text Solution

Verified by Experts

The correct Answer is:
A
`2veca + 3 vecb-5 vecc=0`
`rArr 3(vecb- veca) = 5(vecc- veca) rArr vec(AB) = (5)/(3) vec(AC)`
Hence, `vec(AB) and vec(AC)` must be parallel since there is a common point A. The points A, B and C must be collinear.
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise LINKED COMPREHENSION TYPE|2 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise Exercise (Comprehension)|9 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise Exercise (Multiple)|13 Videos

  • INTEGRALS

    CENGAGE|Exercise Solved Examples And Exercises|324 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Question Bank|24 Videos

Similar Questions

Explore conceptually related problems

Statement 1: if three points P,Q and R have position vectors vec a,vec b, and vec c ,respectively, and 2vec a+3vec b-5vec c=0, then the points P,Q, and R must be collinear.Statement 2: If for three points A,B, and C,vec AB=lambdavec AC, then points A,B, and C must be collinear.

The position vectors of the points A,B,C are vec a, vec b, vec c respectively. If 3 vec a + 2 vec c= 5 vecb , are the points A,B,and C collinear? If so find AB:BC .

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.

If the position vectors of three points are vec a-2vec b+3vec c,2vec a+3vec b-4vec c,-7vec b+10vec c then the three points are

A ,B ,Ca n dD have position vectors vec a , vec b , vec ca n d vec d , respectively, such that vec a- vec b=2( vec d- vec c)dot Then a. A Ba n dC D bisect each other b. B Da n dA C bisect each other c. A Ba n dC D trisect each other d. B Da n dA C trisect each other

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-vec c and 4vec a-7vec b+7vec c are collinear.

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.