A person standing at the crossing at two straight paths represented by the equations 2x-3y-4 = 0 and 3x-4y-5 = 0, wants to reach a path represented by 6x-7y+8 = 0 in least time. Find the equations of path he should follow.
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Solving eq. 2x-3y-4=0 & 3x-4y-5=0
We get,
x=-1 & y=-2
we know that the shortest distance will be perpendicular on the third line from the intersection point.
The slope of third line will be 6/7
Hence, the line of stortest distance will have the slope of -7/6
Therefore eq. of line will be 7x+6y+19=0.
We get,
x=-1 & y=-2
we know that the shortest distance will be perpendicular on the third line from the intersection point.
The slope of third line will be 6/7
Hence, the line of stortest distance will have the slope of -7/6
Therefore eq. of line will be 7x+6y+19=0.
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