Coordinates of a point in space; distance between two points; section formula; direction ratios and direction cosines; angle between two intersecting lines; skew lines; shortest distance between them and its equation; equations of a line and a plane in different forms; intersection of a line and a plane; coplanar lines.
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Q1 · Three-Dimensional Geometry · EASY
The distance between the points A(2, 3, 5) and B(-1, 3, 2) in three-dimensional space is:
Q2 · Three-Dimensional Geometry · EASY
A line passes through the point (2, -1, 3) and has direction ratios proportional to 3, -1, 2. The Cartesian equation of the line is:
Q3 · Three-Dimensional Geometry · MEDIUM
The shortest distance between the skew lines r = (i + 2j + 3k) + λ(i - j + k) and r = (2i - j - k) + μ(-2i + j - 2k) is:
Q4 · Three-Dimensional Geometry · MEDIUM
The angle between the line (x-1)/2 = (y-2)/1 = (z+3)/(-2) and the plane 2x + y - 2z = 5 is:
Q5 · Three-Dimensional Geometry · HARD
The lines (x-1)/2 = (y+1)/3 = z/4 and (x-3)/1 = (y-k)/2 = z/1 intersect if the value of k is: