Three Dimensional Geometry questions
879 published questions with worked solutions.
- Let the image of the point P(2, –1,3) in the plane x + 2y – z = 0 be Q. Then the distance of the plane 3x + 2y + z + 29 = 0 from...
- A(2, 6, 2), B(–4, 0, ), C(2, 3, –1) and D(4, 5, 0), | | 5 are the vertices of a quadrilateral ABCD. If its area is 18 square...
- Let the line L pass through the point (0, 1, 2), intersect the line x-1 2 = y-2 3 = z-3 4 and be parallel to the plane 2x + y –...
- A plane P contains the line of intersection of the plane r .( i + j + k )=6 and r .(2 i +3 j +4 k )=-5. If P passes through the...
- If the lines x-1 2 = 2-y -3 = z-3 and x-4 5 = y-1 2 = z intersect, then the magnitude of the minimum value of 8 is __________.
- If the distance between the plane Ax - 2y + z = d and the plane containing the lines x-1 2 = y-2 3 = z-3 4 and x-2 3 = y-3 4 =...
- If the distance of the point P(1, -2, 1) from the plane x + 2y - 2z = , where > 0, is 5, then the foot of the perpendicular from...
- The point P is the intersection of the straight line joining the points Q(2, 3, 5) and R(1, −1, 4) with the plane 5x − 4y − z =...
- The equation of a plane passing through the line of intersection of the planes x + 2y + 3z = 2 and x − y + z = 3 and at a...
- If the straight lines x - 1 2 = y + 1 k = z 2 and x + 1 5 = y + 1 2 = z k are coplanar, then the plane(s) containing these two...
- Perpendiculars are drawn from points on the line x + 2 2 = y + 1 -1 = z 3 to the plane x + y + z = 3. The feet of perpendiculars...
- A line l passing through the origin is perpendicular to the lines l_1 : (3 + t) i + (-1 + 2t) j + (4 + 2t) k, - < t < l_2 : (3 +...
- Two lines L_1 : x = 5, y 3 - = z -2 and L_2 : x = , y -1 = z 2 - are coplanar. Then α can take value(s)
- Consider the lines L_1 : x - 1 2 = y -1 = z + 3 1 , L_2 : x - 4 1 = y + 3 1 = z + 3 2 and the planes P_1 : 7x + y + 2z = 3, P_2 :...
- From a point P(λ, λ, λ), perpendiculars PQ and PR are drawn respectively on the lines y = x, z = 1 and y = −x, z = −1. If P is...
- In R ^3, consider the planes P_1:y=0 and P_2:x+z=1. Let P_3 be a plane, different from P_1 and P_2, which passes through the...
- In R ^3, let L be a straight line passing through the origin. Suppose that all the points on L are at a constant distance from...
- Consider a pyramid OPQRS located in the first octant (x 0,y 0,z 0) with O as origin, and OP and OR along the x-axis and the...
- Let P be the image of the point (3,1,7) with respect to the plane x-y+z=3. Then the equation of the plane passing through P and...
- The equation of the plane passing through the point (1,1,1) and perpendicular to the planes 2x+y-2z=5 and 3x-6y-2z=7, is
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