If a line makes angles of 90°, 60° and 30° with the positive direction of x, y, and z-axis respectively, find its direction cosines.

If a line has direction ratios 2, –1, –2, determine its cosines.

Find the direction cosines of the line passing through two points (–2,4,–5) and (1,2,3).

Using direction ratios show that the points A(2,3,–4), B(1,–2,3), C(3,8,–11) are collinear.

Find the directional cosines of the sides of the triangle whose vertices are (3,5,–4), (–1,1,2), (–5,–5,–2).

Find the angle between the vectors with direction ratios proportional to 1,–2,1 and 4,3,2.

Find the angle between the vectors with direction ratios proportional to 2,3,–6 and 3,–4,5.

Find the acute angle between the lines whose direction ratios are proportional to 2:3:6 and 1:2:2.

Show that the points (2,3,4), (–1,–2,1), (5,8,7) are collinear.

Show that the line through points (4,7,8) and (2,3,4) is parallel to the line through the points (–1,–2,1) and (1,2,5).

Show that the line through points (1,–1,2) and (3,4,–2) is perpendicular to the line through the points (0,3,2) and (3,5,6).

Show that the line joining the origin to the point (2,1,1) is perpendicular to the line determined by the points (3,5,–1) and (4,3,–1).

Find the angle between the lines whose direction ratios are proportional to a,b,c and b–c, c–a, a–b.

If the coordinates of the points A, B, C, D are (1,2,3), (4,5,7),(–4,3,–6),(2,9,2), then find the angle between AB and CD.

Find the direction cosines of the lines, connected by the relations: l+ m+ n = 0 and 2lm+ 2ln– mn =0.

Find the angle between the lines whose direction cosines are given by the equations:

l+m+n=0 and l²+m²–n²=0

Find the angle between the lines whose direction cosines are given by the equations:

2l–m+2n=0 and mn+nl+lm=0

Find the angle between the lines whose direction cosines are given by the equations:

l+2m+3n=0 and 3lm–4ln+mn=0

Find the angle between the lines whose direction cosines are given by the equations:

2l+2m–n=0 and mn+ln+lm=0

Define direction cosines of a directed line.

What are the direction cosines of X-axis?

What are the direction cosines of Y-axis?

What are the direction cosines of Z-axis?

Write the distance of the point (3, –2, 3) from XY, YZ and XZ planes.

Write the distance of the point (3, –5, 12) from X-axis?

Write the ratio in which YZ-plane divides the segment joining P(–2, 5, 9) and Q(3, –2, 4).

A line makes an angle of 60° with each of X-axis and Y-axis. Find the acute angle made by the line with Z-axis.

If a line makes angles α, β and γ with the coordinate axes, find the value of cos 2α + cos 2β + cos 2γ.

Write the ratio in which the line segment joining (a, b, c) and (-a, -c, -b) is divided by the xy-plane.

Write the inclination of a line with Z-axis, if its direction ratios are proportional to 0, 1, –1.

Write the angle between the lines whose direction ratios are proportional to 1, –2, 1 and 4, 3, 2.

Write the distance of the point P(x, y, z) from XOY plane.

Write the coordinates of the projection of point P(x, y, z) on XOZ-plane.

Write the coordinates of the projection of the point P(2, -3, 5) on Y-axis.

Find the distance of the point (2, 3, 4) from the x-axis.

If a line has direction ratios proportional to 2, -1, -2, then what are its direction consines?

Write direction cosines of a line parallel to z-axis.

Write the distance of a point P(a, b, c) from x-axis.

If a line makes angle 90° and 60° respectively with positive directions of x an y axe, find the angle which it makes with the positive direction of z-axis.