Question

# Find the value of p if the lines, whose equations are $$2x - y + 5 = 0$$ and $$px + 3y = 4$$ are perpendicular to each other.

Solution

## Given line equations,$$2x - y + 5 = 0$$ .......(1)$$y = 2x + 5$$ .......(2)Now,Slope of line $$(2) = 2$$Then, (2) can rewritten as$$3y = -px + 4$$$$y = (-p/3) + 4/3$$So, the slope of this line $$= -p/3$$For 2 lines to be perpendicular to each other, the product of their slopes must be $$-1.$$So,$$(2)\times (-p/3) = -1$$$$2p / 3 = 1$$$$p = 3 / 2$$Maths

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