Two lines 3x+4y=8 and lx+my=n are perpendicular. Which of the following is true?a)3m+4l=0b)3m-4l=0c)3l-4m=0d)3l+4m=0Correct answer is option 'D'. Can you explain this answer?

Question

Answer

In perpendicular, the slope of product = -1
Slope of L1 * slope of L2 = -1
-3/4 * (-l/m) = -1
=> 3l/4m = -1
=> 3l = -4m
= 3l + 4m = 0

Answer

Answer

If two lines are perpendicular then,a1a2+b1b2 a1=3; a2=l ;b1=4;b2=m = 3.l+4.m =3l+4m

Answer

Explanation:

To determine if two lines are perpendicular, we need to check if the product of their slopes is -1.

Given lines:
1) 3x + 4y = 8
2) lx + my = n

Step 1: Convert the given lines into slope-intercept form:

Line 1: 3x + 4y = 8
Rearrange the equation in the form y = mx + c:
4y = -3x + 8
Divide throughout by 4:
y = (-3/4)x + 2

Line 2: lx + my = n
Rearrange the equation in the form y = mx + c:
my = -lx + n
Divide throughout by m:
y = (-l/m)x + (n/m)

Step 2: Compare the slopes of the lines:

The slope of line 1 is -3/4 and the slope of line 2 is -l/m.

To determine if the lines are perpendicular, we need to check if the product of their slopes is -1:

(-3/4) * (-l/m) = 3l/4m

Step 3: Determine the correct option:

The given options are:
a) 3m + 4l = 0
b) 3m - 4l = 0
c) 3l - 4m = 0
d) 3l + 4m = 0

Comparing the product of the slopes (3l/4m) with the options:
- Option a) gives 3m + 4l = 0, which is not equivalent to 3l/4m.
- Option b) gives 3m - 4l = 0, which is not equivalent to 3l/4m.
- Option c) gives 3l - 4m = 0, which is not equivalent to 3l/4m.
- Option d) gives 3l + 4m = 0, which is equivalent to 3l/4m.

Therefore, the correct option is d) 3l + 4m = 0.

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