Question
Download Solution PDFFind the acute angle between the lines 7x - 4y = 0 and 3x - 11y + 5 = 0.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Angle between Two Lines
- The angle θ between the lines having slope m1 and m2 is given by tan θ =
- If the lines are parallel then their slopes are equal. ⇔ m1 = m2
- If the lines are perpendicular then the product of their slope is -1. ⇔ m1 × m2 = -1
Calculation:
We have to find angle between the lines.
Now, let the angle between the given lines 7x - 4y = 0 and 3x - 11y + 5 = 0 is θ
First we need to find the slope of both the lines.
7x - 4y = 0
⇒ y = (7/4) x
Therefore, the slope of the line 7x - 4y = 0 is m1 = 7/4
Again, 3x - 11y + 5 = 0
⇒ y = (3/11) x + (5/11)
Therefore, the slope of the line 3x - 11y + 5 = 0 is m2 = 3/11
We know that tan θ =
⇒ tan θ =
⇒ tan θ = 1 = tan 45°
∴ θ = 45°
Therefore, the required acute angle between the given lines is 45°.
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