CUET UG · Mathematics / Applied Mathematics (Domain)
Direction cosines, equations of lines and planes, angle between them, shortest distance.
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Q1 · Three-Dimensional Geometry · EASY
The direction cosines of a line are proportional to 2, -3, 6. What are the actual direction cosines of the line?
Q2 · Three-Dimensional Geometry · MEDIUM
Find the angle between the line (x - 1)/2 = (y - 2)/3 = (z - 3)/6 and the plane 2x + y - 2z = 5.
Q3 · Three-Dimensional Geometry · EASY
The Cartesian equation of a line passing through (1, -2, 3) and parallel to the vector 3i + 2j - k is:
Q4 · Three-Dimensional Geometry · HARD
Find the shortest distance between the skew lines: L₁: (x - 3)/1 = (y - 8)/(-1) = (z - 3)/1 and L₂: (x + 3)/(-3) = (y + 7)/2 = (z - 6)/4.
Q5 · Three-Dimensional Geometry · HARD
The equation of the plane passing through the point (2, -1, 3) and perpendicular to the vector 4i + 2j - 3k is: