Q. 193.8( 30 Votes )

If the line

Answer :

The equation of the given lines are


y = 3x +1 ------------ (1)


2y = x + 3 ------------- (2)


y = mx + 4 ------------- (3)


Slope of line (1), m1 = 3


Slope of line (2), m2 =


Slope of line (3), m3 = m


It is given that lines (1) and (2) are equally inclined to line (3).


So, the angle between lines (1) and (3) equals between lines (2) and (3).


Thus,






or


Now, if , we get,


(3 – m)(m +2) = (1 – 2m)(1 +3m)


-m2 + m + 6 = 1 + m – 6m2


5m2 + 5 = 0


(m + 1) = 0


m = , which is not real


If , then


(3 – m)(m +2) = - (1 – 2m) (1 +3m)


-m2 + m + 6 = -(1 + m – 6m2)


7m2 + 2m - 7 = 0


m =


m =


m =


Therefore, the required value of m is.


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