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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

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.
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