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Question 117

If the straight lines 5x + 3y + 7 = 0 and ax - 7y + 8 = 0 are perpendicular, then the value of a is

Solution

As per the given equation in the question,

5x + 3y + 7 = 0 and ax - 7y + 8 = 0

Slope of the line 1, $$m_1=\dfrac{3}{5}$$ and slope of line 2, $$m_2=\dfrac{7}{a}$$

When two lines are perpendicular to each other, then $$m_1 \times m_2=-1$$

Now, substituting the values $$\dfrac{3}{5}\times \dfrac{-7}{a}=-1$$

$$a=\dfrac{5}{21}$$

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