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Three Dimensional Geometry
Previous Year Questions (2022-2024)
Year 2022
- Find angle between lines (x-1)/2 = (y+1)/3 = (z-4)/1 and (x-4)/1 = (y-5)/-1 = (z-1)/2.
Show Solution
DR1 = (2,3,1), DR2 = (1,-1,2)\ncosθ = |2(1)+3(-1)+1(2)|/√4+9+1√1+1+4\n= |2-3+2|/√14√6 = 1/2√21\nθ = cos^{-1}(1/2√21) - Find equation of plane through (1,1,1) perpendicular to line with DR (2,3,-1).
Show Solution
Equation: 2(x-1) + 3(y-1) + (-1)(z-1) = 0\n=> 2x + 3y - z - 4 = 0
Year 2023
- Find angle between lines (x-1)/2 = (y+1)/3 = (z-4)/1 and (x-4)/1 = (y-5)/-1 = (z-1)/2.
Show Solution
DR1 = (2,3,1), DR2 = (1,-1,2)\ncosθ = |2(1)+3(-1)+1(2)|/√4+9+1√1+1+4\n= |2-3+2|/√14√6 = 1/2√21\nθ = cos^{-1}(1/2√21) - Find equation of plane through (1,1,1) perpendicular to line with DR (2,3,-1).
Show Solution
Equation: 2(x-1) + 3(y-1) + (-1)(z-1) = 0\n=> 2x + 3y - z - 4 = 0
Year 2024
- Find angle between lines (x-1)/2 = (y+1)/3 = (z-4)/1 and (x-4)/1 = (y-5)/-1 = (z-1)/2.
Show Solution
DR1 = (2,3,1), DR2 = (1,-1,2)\ncosθ = |2(1)+3(-1)+1(2)|/√4+9+1√1+1+4\n= |2-3+2|/√14√6 = 1/2√21\nθ = cos^{-1}(1/2√21) - Find equation of plane through (1,1,1) perpendicular to line with DR (2,3,-1).
Show Solution
Equation: 2(x-1) + 3(y-1) + (-1)(z-1) = 0\n=> 2x + 3y - z - 4 = 0