Three Dimension...

The co-ordinates of the point P are (x, y, z) and the direction cosines of the line OP when O is the origin, are l, m, n. If OP = r, then

A line makes angles α, β, γ with the co-ordinate axis. If α + β = 90°, then γ =

Points (–2, 4, 7), (3, – 6, – 8) and (1, – 2, – 2) are

A line AB in three-dimensional space makes angle 45° and 120° with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle θ with the positive respectively. If AB makes an acute angle θ with the positive z-axis, then θ equals

If projection of any line on co-ordinate axis 3, 4, and 5, then its length is

The direction ratios of the line joining the points (4, 3, – 5) and (–2, 1, – 8) are

The co-ordinates of the point in which the line joining the points (3, 5, – 7) and (–2, 1, 8) is intersected by the plane yz are given by

The direction cosines of the line which is perpendicular to the lines whose direction cosines are proportional to (1, –1, 2) and (2, 1, –1) are