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

Statement 1: Let ` vec a , vec b , vec c and 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

Statement-II and statement II ar correct and Statement III is the correct explanation of statement I

B

Both statement I and statement II are correct but statement II is not the correct explanation of statement I

C

Statement I is correct but statement II is incorrect

D

Statement II is correct but statement I is incorrect

Text Solution

Verified by Experts

The correct Answer is:
A
`3a-2b+5c-6d=(2a-2b)+(-5a+5c)+(6a-6d)`
`=-2AB+5AC-6AD=0`
therefore, AB,AC and AD are linearly dependent.
Hence, by statement II, statement I is true.
Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise For Session 1|7 Videos

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise For Session 2|17 Videos

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

If a, b and c are non-coplanar vectors and d=lambda vec a+mu vec b+nu vec c , then lambda is equal to

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

Let vec a , vec b , vec c , be three non-zero vectors. If vec a .(vec bxx vec c)=0 and vec b and vec c are not parallel, then prove that vec a=lambda vec b+mu vec c ,w h e r elambda are some scalars dot

If vec a , vec b , vec c are mutually perpendicular unit vectors , then find the value of |quad 2 vec a+ vec b+ vec c| .

If vec r* vec a =0 = vec r* vec b ,where vec a and vec b are non-coplanar vectors then

Let vec a and vec b be the position vectors of the points (3,-5) and (m,4) respectively. Find m if the vectors vec a and vec b are collinear.

If vec a , vec b , vec c are three non-coplanar vectors and vec d* vec a = vec d* vec b= vec d* vec c= 0 then show that vec d is zero vector.

If the vectors vec a, vec b, vec c are coplanar then (vec a xx vec b)* vec c = (vec b xx vec c)*vec a =...........

If vec a , vec b , vec c are vectors such that vec adot vec b= vec adot vec c , vec axx vec b= vec axx vec c , vec a!= vec0, then show that vec b= vec c

If the position vector of a point A is vec a + 2 vec b and vec a divides AB in the ratio 2:3 , then the position vector of B, is