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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 Statement I and Statement II are correct and statement II 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
`2a+3b-5c=0`
`3(b-a)=5(c-a)`
`implies AB=(5)/(3)AC`
Hence, AB and AC must be parallel since there is a common point A. the points A,B and C must be collinear.
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