Three Dimensional Geometry questions
879 published questions with worked solutions.
- In and O(0, 0, 0), A(6,2, -3) and B (4,0,3) are the vertices. Let a and b be position vectors of points A and B respectively and...
- If for some m R the lines L_1: x+1 m= y-m -1 = z-1 1 and L_2: x+2 -4 = y+1 9= z+1 1 are coplanar, then line L_1 passes through...
- If the equation of a plane passing through A(1,p,2), B(3,2,4) and parallel to the z axis, is 3x-2y-q=0, then.............
- If the plane 2x+3y+z=6 cuts coordinate axes at A, B and C, then the volume of tetrahedron OABC (where O is the origin) is _____...
- The coordinates of the point of intersection of the lines x-3 1 = y-5 2 = z-1 -1 and x-4 2 = y-2 -1 = z-4 2 are…
- If the plane r =( + ) i +(2+ ) j +(3 +2 ) k , where and are parameters, intersects coordinate axes at points (a, 0, 0), (0, b, 0)...
- The acute angle between the xy-plane and the plane passing through the point (1, 2, 4) and parallel to the vectors with direction...
- The line passes through the point (2, 1, 1) and is parallel to the plane x + y + 2z = 18. If line intersects the line x+2 3 = y+1...
- The lines x-3 1 = y-2 1 = z-5 -k and x-4 k = y-3 1 = z-3 2 are coplanar, hence k =
- The projection of the line segment joining the points (2, 1, -3) and (-1, 0, 2) on the line whose direction ratios are 3, 2, 6 is
- A plane passes through (2, 1, 2) and (1, 2, 1) and parallel to the line 2x = 3y and z = 1, then the plane also passes through the...
- The equation of the plane passing through the line of intersection of the planes x + y + z = 1 and 3x + 4y + 5z = 2 and...
- The Cartesian equation of plane through A (7, 8, 6) and parallel to the XY plane is
- The distance of the point (-3, 2, 3) from the line passing through (4, 6, -2) and having direction ratios -1, 2, 3 is _____ units
- A plane passes through (1, -2, 1) and is perpendicular to the planes 2x - 2y + z = 0 and x - y + 2z = 4. The distance of the...
- If the sum of the squares of the distance of the point P(x, y, z) from the co-ordinate axes is 242, then the distance of the...
- If the points A(2-x,2,2), B(2,2-y,2), C(2,2,2-z) and D(1,1,1) are coplanar, then the locus of point P(x,y,z) is
- If the lines 3-x 2 = 5y-2 3 +1 =5-z and x+2 -1 = 1-3y 7 = 4-z 2 are at right angles, then 7 -10 =
- If the angle between the line x+1 1 = y-1 2 = z-2 2 and the plane 2x-y+ ,z+4=0 is such that = 13, then +1=
- If the directed line makes an angle 45^0 and 60^0 with the X and Y-axes respectively, then the obtuse angle made by the line with...
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