Question

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

Answer 1

Correct Answer - 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.