Home
Class 12
MATHS
Statement 1: Let vec a , vec b , vec ca...

Statement 1: Let ` vec a , vec b , vec ca n d vec d` be the position vectors of four points `A ,B ,Ca n dD` and `3 vec a-2 vec b+5 vec c-6 vec d=0.` Then points `A ,B ,C ,a n dD` are coplanar. Statement 2: Three non-zero, linearly dependent coinitial vector `( vec P Q , vec P Ra n d vec P S)` are coplanar. Then ` vec P Q=lambda vec P R+mu vec P S ,w h e r elambdaa n dmu` are scalars.

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
` 3 veca - 2vecb + 5vecc - 6 vecd = ( 2veca - 2vecb)+ (-5vec a+ 5 vecc) + ( 6veca - 6 vecd) `
`" " = - 2 vec(AB) + 5vec(AC) - 6 vec(AD) - 6 vec(AD) = vec0`
Therefore, `vec(AB) , vec(AC) and vec(AD)` are linearly dependent.
Hence by Statement 2, Statement 1 is true.
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

Let vec a,vec b,vec c,vec d be the position vectors of the four distinct points A,B,C,D. If vec b-vec a=vec a-vec d, then show that ABCD is parallelogram.

vec a,vec b,vec c,vec d are the position vectors of the four distinct points A,B,C, D respectively.If vec b-vec a=vec c-vec d, then show that ABCD is a parallelogram.

If vec a , vec b , vec c and vec d are the position vectors of points A, B, C, D such that no three of them are collinear and vec a + vec c = vec b + vec d , then ABCD is a

If vec a,vec b,vec c are the position vectors of points A,B,C and D respectively such that (vec a-vec d)*(vec b-vec c)=(vec b-vec d)*(vec c-vec a)=0 then D is the

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

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

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

The position vectors of three points are 2vec a-vec b+3vec c,vec a-2vec b+xvec c and yvec a-5vec b where vec a,vec b,vec c are non coplanar vectors.If the three points are collinear then

If vec a,vec b,vec c and vec d are the position vectors of the points A,B,C and D respectively in three dimensionalspace no three of A,B,C,D are collinear and satisfy the relation 3vec a-2vec b+vec c-2vec d=0, then

If vec a , vec b , vec c are three non coplanar vectors such that vec ddot vec a= vec ddot vec b= vec ddot vec c=0, then show that d is the null vector.