Correct Answer – Option 2 : -2/3

Concept: 

Let the one line has slope m₁ and the second line has slope m₂.

If two straight lines are perpendicular then the multiplication of their slopes will be -1, that is “m₁m₂ = -1″.

Calculation:

Compare both the given equation with the standard form, y = mx + c.

The slope, m₁ for the line, 2x + 3y – 3 = 0 is, \(- \frac{2}{3}\).

The slope, m2 for the line, x + ky + 7 = 0 is, \( \rm- \frac{1}{k}\).

As both the equations are perpendicular, so m1m2 = -1

\(\rm\left( { – \frac{2}{3}} \right)\left( { – \frac{1}{k}} \right) = – 1\)

⇒ \(\rm \frac{2}{{3k}} = – 1\)

⇒ \(\rm k = – \frac{2}{3}\)