PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

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.

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