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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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