NCERT Class 11 Mathematics Solutions: Chapter 10 –Straight Lines Miscellaneous Exercise 10 Part 10

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Angle between two lines

Angle Between Two Lines

Angle between two lines

1. If the lines are equally inclined to the line , find the value of .

Answer:

The equations of the given lines are

…………………….. eq (1)

…………………….. eq (2)

……………………. eq (3)

Slope of line

Slope of line

Slope of line

It is given that lines (1) and (2) are equally inclined to line (3).

This means that the angle between lines (1) and (3) equals the angle between lines (2) and (3).

Or

If then

, which is not real.

Hence, this case is not possible.

If , then

So, the required value of is