Commerce (English Medium) इयत्ता १२ - CBSE Question Bank Solutions

If the coordinates of the points A, B, C, D are (1, 2, 3), (4, 5, 7), (−4, 3, −6) and (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
(i) 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, 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.