| Direction: For the following questions, chose the correct answer from the codes [a], [b] [c] and [d] defined as follows. |
| Let there are three points P, Q and R having position vectors a, b and c, respectively. |
| Statement I If \[2a+3b-5c=0\], then points P, Q and R must be collinear. |
| Statement II For three points A, B and C; \[AB=\lambda AC,\] then the points A, B and C must be collinear. |
A) Statement I is true, Statement II is also true and Statement II is the correct explanation of Statement I.
B) Statement I is true, Statement II is true and Statement II is not the correct explanation of Statement I.
C) Statement I is true, Statement II is false.
D) Statement I is false, Statement II is true.
Correct Answer: A
Solution :
I. \[OP=a,\,\,OQ=b,\,\,OR=c\] Given, \[2a+3b-5c=0\] \[\Rightarrow \] \[3(b-a)+5(a-c)=0\] \[\Rightarrow \] \[3(OQ-OP)=5(OR-OP)\] \[\Rightarrow \] \[3PQ=5PR\] \[\Rightarrow \] \[PQ=\frac{5}{3}PR\] P, Q and R are collinear.
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