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On the xy plane where O is the origin, g...

On the xy plane where O is the origin, given points, A(1,0), B(0,1) and C(1,1). Let P,Q, and R be moving points on the line OA, OB, OC respectively such that `vec(OP)=45t(vec(OA)), vec(OQ)=60t(vec(OB)), vec(OR)=(1-t)(vec(OC))` with `t gt 0`. If the three points P,Q and R are collinear then the value of t is equal to

A

`1/106`

B

`7/187`

C

`1/100`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Again it is given that the point P,Q and R are collinear
`rArr vec(PQ) = lambdavec(QR)`
`rArr 15r(4vecj-3veci)=lambda[(1-t)(hati+hatj)-60thatj]`
`=lambda[(1-t)hati+(1-6lthatj)]`
`rArr (45t)/(t-1) = (4t)/(1-61t)`
`rArr 3(1-61t)=4(t-1)`
`rArr 3-183t=4t-4`
`rArr 187t=7`
`rArr t=7/187`
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