Commerce (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

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

2l + 2m − n = 0, 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 distances of the point (7, −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 cos2α + cos2β + cos2γ.

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.

If a unit vector  `vec a` makes an angle \[\frac{\pi}{3} \text{ with } \hat{i} , \frac{\pi}{4} \text{ with }  \hat{j}\] and an acute angle θ with \[\hat{ k} \] ,then find the value of θ.