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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

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.
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