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 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.

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 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.
Answer» Correct Answer - A `2veca + 3 vecb-5 vecc=0` `rArr 3(vecb- veca) = 5(vecc- veca) rArr vec(AB) = (5)/(3) vec(AC)` Hence, `vec(AB) and vec(AC)` must be parallel since there is a common point A. The points A, B and C must be collinear.

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