Three Dimensional Geometry questions
879 published questions with worked solutions.
- The distance between the planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is
- A perpendicular PQ is dropped from the point P(1, 2, 3) to the plane x + y + z = 3, Q being the foot. Then
- A plane passes through (1, -2, 1) and is perpendicular to the planes 2x - 2y + z = 0 and x - y + 2z = 4. Then the distance of...
- Let AB be a chord of the circle x^2 + y^2 = r^2 subtending a right angle at the centre. Then the locus of the centroid of the PAB...
- More than one may match with the same. Column I: (i) If _ n=1 ^ ^ -1 1 2n^2 = t then t equals (ii) If in the ABC the sides a, b,...
- Consider the planes 3x - 6y - 2z = 15 and 2x + y - 2z = 5. STATEMENT-1: The parametric equations of the line of intersection of...
- Let P(3, 2, 6) be a point in space and Q be a point on the line r = ( i - j + 2 k) + (-3 i + j + 5 k). Then the value of for...
- A line with positive direction cosines passes through the point P(2, -1, 2) and makes equal angles with the coordinate axes. The...
- The equation of the plane containing the straight line x 2 = y 3 = z 4 and perpendicular to the plane containing the straight...
- 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 P...
- 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 =...
- The distance of the point (1, 0, 2) from the point of intersection of the line x-2 3 = y+1 4 = z-2 12 and the plane x − y + z =...
- The equation of the plane containing the line of intersection of 2x - 5y + z = 3; x + y + 4z = 5, and parallel to the plane, x +...
- If the points (1, 1, ) & (-3, 0, 1), are equidistant from the plane, 3x+4y-12z+13 = 0, then satisfies the equation:
- A plane containing the point (3,2,0) and the line x-1 1 = y-2 5 = z-3 4 also contains the point
- The distance of the point (1,-2,4) from the plane passing through the point (1,2,2) and perpendicular to the planes x-y+2z = 3...
- The number of distinct real values of , for which the lines x-1 1 = y-2 2 = z+3 ^2 and x-3 1 = y-2 ^2 = z-1 2 , are coplanar is
- The coordinates of the foot of the perpendicular from the point (1,-2,1) on the plane containing the lines x+1 6 = y-1 7 = z-3 8...
- The line of intersection of the planes r (3 i - j + k ) = 1 and r ( i + 4 j - 2 k ) = 2, is:
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