Question

Let O be the origin and let P be a point on the line \(x + \sqrt{3}y = 10\). If OP is perpendicular to the line, then the angle between OP and the y-axis is

• A. \(15^\circ\)
• B. \(30^\circ\)
• C. \(45^\circ\)
• D. \(60^\circ\)
• E. \(75^\circ\)

Hint:

For a line in general form \(ax + by = c\), the angle its normal (perpendicular) makes with the x-axis is given by \(\tan \phi = b/a\). Here, \(\tan \phi = \sqrt{3}/1 = \sqrt{3}\), so \(\phi = 60^\circ\). The angle with the y-axis is then \(90^\circ - 60^\circ = 30^\circ\).

Answer 1

The Correct Option is B