Three Dimensional Geometry questions
879 published questions with worked solutions.
- The foot of perpendicular form the origin O to a plane P which meets the co-ordinate axes at the points A, B, C is (2, a, 4), a...
- Let P be the plane, passing through the point (1,–1,–5) and perpendicular to the line joining the points (4,1,–3) and (2, 4, 3)....
- Let the plane P : 8x+a_1y+a_2z+12=0 be parallel to the line L : x+2 2 = y-3 3 = z+4 5 . If the intercept of P on the y-axis is 1,...
- Let the line L : x-1 2 = y+1 -1 = z-3 1 intersect the plane 2x + y + 3z = 16 at the point P. Let the point Q be the foot of...
- 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 μ for...
- A line with positive direction cosines passes through the point P(2, −1, 2) and makes equal angles with the coordinate axes. The...
- Let L_1 be the line of intersection of the planes given by the equations 2x + 3y + z = 4 and x + 2y + z = 5. Let L_2 be the line...
- A plane which passes through the point (3, 2, 0) and the line x-4 1 = y-7 5 = z-4 4 is
- The d.r. of normal to the plane through (1, 0, 0), (0, 1, 0) which makes an angle /4 with plane x + y = 3 are
- The lines x-2 1 = y-3 1 = z-4 -k and x-1 k = y-4 1 = z-5 1 are coplanar if
- A tetrahedron has vertices at O(0, 0, 0), A(1, 2, 1) B(2, 1, 3) and C(-1, 1, 2). Then the angle between the faces OAB and ABC...
- Two system of rectangular axes have the same origin. If a plane cuts them at distances a, b, c and a', b', c' from the origin then
- A line makes the same angle , with each of the x and z axis. If the angle , which it makes with y-axis, is such that ^2 = 3 ^2 ,...
- If the straight lines x = 1 + s, y = -3 - s, z = 1 + s and x = t 2 , y = 1 + t, z = 2 - t with parameters s and t respectively,...
- A line with direction cosines proportional to 2, 1, 2 meets each of the lines x = y + a = z and x + a = 2y = 2z. The co-ordinates...
- The intersection of the spheres x^2 + y^2 + z^2 + 7x - 2y - z = 13 and x^2 + y^2 + z^2 - 3x + 3y + 4z = 8 is the same as the...
- 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 = 1 3 the value of is
- If the plane 2ax - 3ay + 4az + 6 = 0 passes through the midpoint of the line joining the centres of the spheres x^2 + y^2 + z^2 +...
- The two lines x = ay + b, z = cy + d; and x = a'y + b', z = c'y + d' are perpendicular to each other if
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