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

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.

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the distance of a point P(a, b, c) from x-axis.

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

For every point P (x, y, z) on the xy-plane,

For every point P (x, y, z) on the x-axis (except the origin),

A rectangular parallelopiped is formed by planes drawn through the points (5, 7, 9) and (2, 3, 7) parallel to the coordinate planes. The length of an edge of this rectangular parallelopiped is

A parallelopiped is formed by planes drawn through the points (2, 3, 5) and (5, 9, 7), parallel to the coordinate planes. The length of a diagonal of the parallelopiped is

The xy-plane divides the line joining the points (−1, 3, 4) and (2, −5, 6)

If the x-coordinate of a point P on the join of Q (2, 2, 1) and R (5, 1, −2) is 4, then its z-coordinate is

The distance of the point P (a, b, c) from the x-axis is 

Ratio in which the xy-plane divides the join of (1, 2, 3) and (4, 2, 1) is

If P (3, 2, −4), Q (5, 4, −6) and R (9, 8, −10) are collinear, then R divides PQ in the ratio

If O is the origin, OP = 3 with direction ratios proportional to −1, 2, −2 then the coordinates of P are

The angle between the two diagonals of a cube is

If a line makes angles α, β, γ, δ with four diagonals of a cube, then cos² α + cos² β + cos²γ + cos² δ is equal to