• # question_answer 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.

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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