What is the angle made by the line L with positive direction of y-axis ?
For the next two (02) items that follow : The equation of a straight line which passes through the origin and makes an angle \( \alpha \) (\( 0 \le \alpha \le 90^\circ \)) with the line \( L : x + \sqrt{3}y + 3\sqrt{3} = 0 \) is \( x - \sqrt{3}y = 0 \).
- A. 30^\circ
- B. 45^\circ
- C. 60^\circ ✓
- D. 90^\circ
Correct Answer: C. 60^\circ
Explanation
The line L has a slope of -1/\sqrt{3}, meaning it makes an angle of 150^\circ with the positive x-axis. Its angle with the positive y-axis is 150^\circ - 90^\circ = 60^\circ.
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