NCERT Class 11 Mathematics Solutions: Chapter 10 –Straight Lines Miscellaneous Exercise 10 Part 6

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The angle between two lines

The Angle Between Two Lines

The angle between two lines

1. If three lines whose equations are are concurrent show that

Answer:

The equations of the given lines are

……………………. eq (1)

………………….… eq (2)

……………………. eq (3)

On subtracting equation (1) from (2)

On substituting this value of in eq (1)

is the point of intersection of lines (1) and (2).

It is given that lines (1), (2), and (3) are concurrent.

Hence, the point of intersection of lines (1) and (2) will also satisfy equation (3).

2. Find the equation of the lines through the point which make an angle of with the line .

Answer:

Consider the slope of the required line be .

The given line can be written as , which is of the form

Slope of the given line

It is given that the angle between the required line and line .

We know that if θ is the acute angle between lines with slopes , then

Case I:

The equation of the line passing through and having a slope of 3 is:

Case II:

The equation of the line passing through and having a slope of is:

So, the equation of the lines are .