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  4. On the xy plane where O is the origin, given points, A(1,0), B(0,1) and C(1,1). Let P, Q, R be moving points on the line OA , OB , OC respectively such that OP =45 t ( OA ), OQ =60 t ( OB ), OR =(1-t)( OC ) with t >0. If f(t)=|P Q| then the differential coefficient of f(t) when t=1, is equal to

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Q. On the xy plane where $O$ is the origin, given points, $A(1,0), B(0,1)$ and $C(1,1)$. Let $P, Q, R$ be moving points on the line $OA , OB , OC$ respectively such that $\overrightarrow{ OP }=45 t (\overrightarrow{ OA }), \overrightarrow{ OQ }=60 t (\overrightarrow{ OB })$, $\overrightarrow{ OR }=(1-t)(\overrightarrow{ OC })$ with $t >0$.
If $f(t)=|\overrightarrow{P Q}|$ then the differential coefficient of $f(t)$ when $t=1$, is equal to

Vector Algebra

Solution:

Correct answer is (c) 75