Condition for Perpendicular Lines in General Form

Rarely Tested

Condition for Perpendicular Lines in General Form

## Formula

For:

$$A_1x+B_1y+C_1=0$$

and:

$$A_2x+B_2y+C_2=0$$

the lines are perpendicular if:

$$A_1A_2+B_1B_2=0$$

## Usage

- Used to test whether two lines are perpendicular directly from their coefficients.

Question 1

Let the lines

$$L_1:(k-1)x+y=5$$ and $$L_2:x+(k+1)y=7$$ be perpendicular to each other. Then the value of $$k$$ is :

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