Statement 1: if threepoints `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 threepoints `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 IB. Both statement I and statement II are correct but statement II is not the correct explanation of statement IC. Statement I is correct but statement II is incorrectD. Statement II is correct but statement I is incorrect

Statement 1: if threepoints `P ,Qa n dR`have position vectors ` vec a

1.	Statement 1: if threepoints `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 threepoints `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 IB. Both statement I and statement II are correct but statement II is not the correct explanation of statement IC. Statement I is correct but statement II is incorrectD. Statement II is correct but statement I is incorrect
Answer» 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.

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