Q28 of 29 Page 1

Find the distance of the point ( – 1, – 5, – 10) from the point of intersection of the line and the plane

Here we have the cartesian equation of a line,


And, the cartesian equation of a plane,


x – y + z – 5 = 0.


Let Q(be the point of intersection of line and plane which will satisfy both equation.


(let)



also




So, putting the value of , we get,





And,




Q = (2, – 1, 2)


l(PQ) =



= 13 units.

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OR


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Evaluate

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Evaluate .

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A factory manufactures two types of screws A and B, each type requiring the use of two machines, an automatic and a hand – operated. It takes 4 minutes on the automatic and 6 minutes on the hand operated machines to manufacture a packet of screws ‘B’. Each machine is availble for at most 4 hours on any day. The manufacturer can sell a packet of screws ‘A’ at a profit of 70 paise and screws ‘B’ at a profit of Rs. 1. Assuming that he can sell all the screws he manufactrures, how many packets of each type should the factory owner produce in a day in order to maximize his profit ? Formulate the above LPP and solve it graphically and find the maximum profit.