Three Dimensions Mock Tests

The direction cosines of the line joining (1, 0, 2) and (2, 2, 0) are:

The distance between the points (1, 2, 3) and (4, 6, 7) is:

The equation of a plane passing through the origin with normal vector 2i - j + 2k is:

The vector equation of a line passing through point with position vector 2î + ĵ − k̂ and parallel to vec(b) = î − 2ĵ + 3k̂ is:

The angle between the line (x−1)/3 = (y−2)/2 = (z−3)/−2 and the y-axis is:

The shortest distance between the lines (x-1)/2 = (y-2)/3 = (z-1)/4 and (x-2)/3 = (y-3)/4 = (z-4)/5 is:

The shortest distance between the lines (x − 1)/2 = (y − 2)/3 = (z − 3)/4 and (x − 2)/3 = (y − 3)/4 = (z − 5)/5 is:

The direction cosines of the line passing through points (1, -1, 2) and (3, -4, 5) are: