Question

The value of k for which the lines 2x + 3y + 7 = 0 and
11x + ky + 25 = 0 are perpendicular, is :
​

Answer 1

Answer:

See below.

Step-by-step explanation:

We are given two lines,

$2x + 3y + 7 = 0\\11x + ky + 25 = 0$

Both the lines are perpendicular to each other. Hence the product of their slopes will be -1.

So, slope of line 1:

$= - \frac{2}{3}$

Slope of line 2:

$= - \frac{11}{k}$

The product of their slopes is -1:

$(-\frac{2}{3})(- \frac{11}{k} ) = -1\\\frac{22}{3k} = -1\\k = - \frac{22}{3}$

Therefore, the value of k is,

$k =- \frac{22}{3}$