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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 `overline(OP)=45t overline((OA)),overline(OQ)=60t overline((OB)),overline(OR)=(1-t) overline((OC))` with `t>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

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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