Question

The angle between the lines 3x+2y=5and2x-3y=7

Answer 1

Answer:

Take the Explanation for better understanding.

Step-by-step explanation:

Method 1:

If the two lines are a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, then the formula to find the angle between them becomes

tan θ = |(a1b2 - b1a2)/(a1a2 + b1b2)|

3x + 2y = 5 ..........(1)

3x + 2y - 5 = 0

Then a1 = 3, b1 = 2, c1 = -5

2x - 3y = 7 ..............(2)

2x - 3y -7 = 0

Then a2 = 2, b2 = -3, c2 = -7

tan θ = |(3*(-3) - 2*2)/(3*2 + 2*(-3))|

tan θ = |-13/0|

tan θ = infinity

So, angle θ = 90 degree.

Both lines are perpendicular to each other.

Method 2:

Slope  of line 1 is

m1 = -a1/b1 = -3/2

Slope of line 2 is

m2 = -a2/b2 = -2/-3 = 2/3

Since, m1 = -1/m2

Two lines are perpendicular to each other if slope of one line is negative reciprocal of slope of second line. (m1 = -1/m2)

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