Three Dimensional Geometry questions
879 published questions with worked solutions.
- The distance of the point (5,3,-1) from the plane passing through points (2,1,0), (3,-2,4) and (1,-3,3) is
- The equation of a line passing through the point (-1,2,3) and perpendicular to the lines x2= y-1 -3 = z+2 -2 and x+3 -1 = y+3 2 =...
- A line L is passing through points A(1,3,2) and B(2,2,1). If mirror image of point P(1,1,-1) in the line L is (x,y,z) then x+y+z=
- ABCD is parallelogram. The position vectors of A and C are respectively, 3 i + 3 j + 5 k and i - 5 j - 5 k. If M is the midpoint...
- The values of a for which the two points (1, a, 1) and (−3, 0, a) lie on the opposite sides of the plane 3x + 4y − 12z + 13 = 0,...
- Statement 1: If the points (1, 2, 2), (2, 1, 2) and (2, 2, z) and (1, 1, 1) are coplanar, then z = 2. Statement 2: If the 4...
- The coordinates of the foot perpendicular from the point (1, 0, 0) to the line x - 1 2 = y + 1 -3 = z + 10 8 are
- If the three planes x = 5, 2x − 5ay + 3z − 2 = 0 and 3bx + y − 3z = 0 contain a common line, then (a, b) is equal to
- Consider the following planes P : x + y - 2z + 7 = 0 Q : x + y + 2z + 2 = 0 R : 3x + 3y - 6z - 11 = 0
- The equation of a plane containing the line x + 1 -3 = y - 3 2 = z + 2 1 and the point (0, 7, −7) is
- An equation of a plane parallel to the plane x − 2y + 2z − 5 = 0 and at a unit distance from the origin is
- If the lines x - 1 2 = y + 1 3 = z - 1 4 and x - 3 1 = y - k 2 = z1 intersect, then k is equal to
- If the lines x - 2 1 = y - 3 1 = z - 4 -k and x - 1 k = y - 4 2 = z - 5 1 are coplanar, then k can have
- If the lines x + 1 2 = y - 1 1 = z + 1 3 and x + 2 2 = y - k 3 = z4 are coplanar, then the value of k is :
- The acute angle between two lines such that the direction cosines l, m, n, of each of them satisfy the equations l + m + n = 0...
- Let Q be the foot of perpendicular from the origin to the plane 4x − 3y + z + 13 = 0 and R be a point (−1, 1, −6) on the plane....
- The equation of a plane through the line of intersection of the planes x + 2y = 3, y − 2z + 1 = 0, and perpendicular to the first...
- Equation of the plane which passes through the point of intersection of lines x-1 3 = y-2 1 = z-3 2 and x-3 1 = y-1 2 = z-2 3 and...
- A line in the 3-dimensional space makes an angle (0 < 2 ) with both the X and Y−axes. Then, the set of all values of θ is in the...
- Let A(2, 3, 5), B(-1, 3, 2) and C( , 5, ) be the vertices of a ABC. If the median through A is equally inclined to the coordinate...
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