Angle between Two Lines
Angle between Two Lines: Overview
This topic covers concepts such as Angle between Lines in Vector Form, Angle between Two Lines in 3D, Parallel Lines in 3D, and Perpendicular Lines in 3D.
Important Questions on Angle between Two Lines
The equation of the perpendicular drawn from the point to the line is :

The angle between the lines and is

The measure of acute angle between the lines whose direction ratios are and is

Find the acute angle between the line joining points and and the line having direction ratios . [Enter the value in degrees excluding degree symbol]

Find the angle between the pair of lines and .

If and are direction cosines of three mutually perpendicular lines , show that the line whose direction cosines are proportional to makes equal angles with lines and .

Directions ratios of two lines satisfy the relation and . Show that the lines are perpendicular.

Find the direction cosines of the line which is perpendicular to the lines with direction ratios and .

Find the angle between the lines whose direction ratios are and . [Enter the value in degrees excluding degree symbol]

If the direction ratios of two vectors are connected by the relations and find the angle between them.

Find the direction cosines of the vector which is perpendicular to the vectors with direction ratios and .

Find the direction ratios of a vector perpendicular to the two lines whose direction ratios are and .

If a line drawn from the point is perpendicular to the line joining and then find the coordinates of the foot of the perpendicular.

Find , if is right angled at where .

Find if is right angled at where .

Show that the vector is perpendicular to where and .

If the angle between the vectors and having direction ratios and is find .

Find the measure of acute angle between the lines whose direction ratios are and .

Find the measure of acute angle between the lines whose direction ratios are and .

If the lines and are perpendicular to each other, then
