Three Dimensional Geometry questions
879 published questions with worked solutions.
- If the image of the point (4, 4, 3) in the line x-1 2 = y-2 1 = z-1 3 is ( , , ), then + + is equal to
- The square of the distance of the point ( 15 7 , 32 7 ,7 ) from the line x+1 3 = y+3 5 = z+5 7 in the direction of the vector i...
- If A and B are the points of intersection of the circle x^2+y^2-8x=0 and the hyperbola x^2 9 - y^2 4 =1 and a point P moves on...
- Let L_1 : x-1 1 = y-2 -1 = z-1 2 and L_2 : x+1 -1 = y-2 2 = z 1 be two lines. Let L_3 be a line passing through the point ( , , )...
- Let a straight line L pass through the point P(2, –1, 3) and be perpendicular to the lines x-1 2 = y+1 1 = z-3 -2 and x-3 1 = y-2...
- Let P be the foot of the perpendicular from the point (1, 2, 2) on the line L : x-1 1 = y+1 -1 = z-2 2 . Let the line r = (- i+...
- Each of the angles and that a given line makes with the positive y and z-axes, respectively, is half of the angle that this line...
- The distance of the point (7, 10, 11) from the line x-4 1 = y-4 0 = z-2 3 along the line x-9 2 = y-13 3 = z-17 6 is
- Let a line passing through the point (4, 1, 0) intersect the line L_1 : x-1 2 = y-2 3 = z-3 4 at the point A(α, β, γ) and the...
- Let A and B be two distinct points on the line L : x-6 3 = y-7 2 = z-7 -2 . Both A and B are at a distance 2 17 from the foot of...
- Let the area of the triangle formed by the lines x+2 = y-1 = z, x-3 5 = y -1 = z-1 1 and x -3 = y-3 3 = z-2 1 be A. Then A^2 is...
- Let the three sides of a triangle ABC be given by the vectors 2 i - j + k , i - 3 j - 5 k and 3 i - 4 j - 4 k . Let G be the...
- Consider the lines L_1 : x - 1 = y - 2 = z and L_2 : x - 2 = y = z - 1. Let the feet of the perpendiculars from the point P(5, 1,...
- The image of the line x - 1 3 = y - 3 1 = z - 4 -5 in the plane 2x - y + z + 3 = 0 is the line:
- The angle between the lines whose direction cosines satisfy the equations + m + n = 0 and ^2 = m^2 + n^2 is -
- The distance of the point (1, –5, 9) from the plane x – y + z = 5 measured along the line x = y = z is :
- If the line, x - 3 2 = y + 2 -1 = z + 4 3 lies in the plane, ℓx + my – z = 9, then ^2 + m^2 is equal to :
- The distance of the point (1, 3, –7) from the plane passing through the point (1, –1, –1), having normal perpendicular to both...
- If L_1 is the line of intersection of the planes 2x - 2y + 3z - 2 = 0, x - y + z + 1 = 0 and L_2 is the line of intersection of...
- The sum of the intercepts on the coordinate axes of the plane passing through the point (–2, –2, 2) and containing the line...
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