Mathematics › 3D Coordinate Geometry
3D Coordinate Geometry Questions
101 questions across 7 subtopics — with step-by-step solutions.
Angle between two planes(6)
- Let a_{1} x+b_{1} y+c_{1} z+d_{1}=0 and a_... | Mathematics | TestHub
- A plane passes through (1,0,0) and (0,1,0)... | Mathematics | TestHub
- Let a_{1} x+b_{1} y+c_{1} z+d_{1}=0 and a_... | Mathematics | TestHub
- A tetrahedron has vertices at O(0,0,0), A(... | Mathematics | TestHub
- Let a_{1} x+b_{1} y+c_{1} z+d_{1}=0 and a_... | Mathematics | TestHub
- Angle \theta is made by line of intersecti... | Mathematics | TestHub
Coordinates of a point in space, Direction cosines,(29)
- The curve described parametrically by repr... | Mathematics | TestHub
- If and are respectively the magnitudes of... | Mathematics | TestHub
- A line making angles and with the positive... | Mathematics | TestHub
- If a line segment makes angles of and with... | Mathematics | TestHub
- The radius of the sphere is | Mathematics | TestHub
- If l_{i}^{2}+m_{i}^{2}+n_{i}^{2}=1 \forall... | Mathematics | TestHub
- The direction cosines of two lines are con... | Mathematics | TestHub
- For A=(3,4,2), B=(3,0,2) and C=(5,0,0) , w... | Mathematics | TestHub
- The two lines whose direction cosines are... | Mathematics | TestHub
- The coordinates of the point equidistant f... | Mathematics | TestHub
- If l_{1}, m_{1}, n_{1} and l_{2}, m_{2}, n... | Mathematics | TestHub
- The coordinates of the circumcentre of the... | Mathematics | TestHub
- A rectangle ABCD of dimensions r and 2r is... | Mathematics | TestHub
- In a three dimensional co-ordinate system... | Mathematics | TestHub
- Given that the points A(3,2,-4), B(5,4,-6)... | Mathematics | TestHub
- If A(0,1,2), B(2,-1,3) and C(1,-3,1) are t... | Mathematics | TestHub
- A, B, C are the points on x, y and z axes... | Mathematics | TestHub
- Match the following.List-IList-II(A) Lengt... | Mathematics | TestHub
- The volume of a right triangular prism A B... | Mathematics | TestHub
- A rectangle ABCD of dimensions r and 2r is... | Mathematics | TestHub
- The four lines drawn from the vertices of... | Mathematics | TestHub
- The ratio in which the y z plane divides t... | Mathematics | TestHub
- The points (0, 7, 10), (- 1, 6, 6) and (-... | Mathematics | TestHub
- Match the following.List-IList-II(A) If in... | Mathematics | TestHub
- f(x) be a polynomial in x satisfying the c... | Mathematics | TestHub
- The ratio in which the plane 2 x-1=0 divid... | Mathematics | TestHub
- If the median through A of \triangle A B C... | Mathematics | TestHub
- Let ABCD be a tetrahedron in which positio... | Mathematics | TestHub
- Three straight lines mutually perpendicula... | Mathematics | TestHub
Coplanarity of two lines(9)
- Statement 1 - The lines \frac{x-2}{1}=\fra... | Mathematics | TestHub
- If the lines \frac{x-1}{2}=\frac{y-2}{x_{1... | Mathematics | TestHub
- The lines \frac{x-a+d}{\alpha-\delta}=\fra... | Mathematics | TestHub
- Lines L_{1}: \frac{x-3}{2}=\frac{y-2}{3}=\... | Mathematics | TestHub
- Statement 1 - The lines \frac{x+1}{1}=\fra... | Mathematics | TestHub
- Statement-1: The lines \frac{x-1}{1}=\frac... | Mathematics | TestHub
- The points A(2-x, 2,2), B(2,2-y, 2), C(2,2... | Mathematics | TestHub
- Two lines whose equations are \frac{x-3}{2... | Mathematics | TestHub
- Statement 1 - Consider the lines L_{1}: \f... | Mathematics | TestHub
Equation of the bisector planes, Angle between two planes(2)
Family of planes(9)
- Let P_1 be the plane x+2y-z-1=0 and P_2 be... | Mathematics | TestHub
- The plane 3 x+4 y=0 is rotated through an... | Mathematics | TestHub
- Find the x -intercept of the plane through... | Mathematics | TestHub
- If P_{1}=0 and P_{2}=0 are the equations o... | Mathematics | TestHub
- An equation of the plane passing through t... | Mathematics | TestHub
- The plane l x+m y=0 is rotated about its l... | Mathematics | TestHub
- If P_{1}=0 and P_{2}=0 are the equations o... | Mathematics | TestHub
- If P_{1}=0 and P_{2}=0 are the equations o... | Mathematics | TestHub
- The plane x-y-z=4 is rotated through 90^{\... | Mathematics | TestHub
Perpendicular distance of a point from a plane(20)
- A regular tetrahedron has edge length \ell... | Mathematics | TestHub
- Match the following.List-IList-II(A) Foot... | Mathematics | TestHub
- Let A(1,1,1), B(2,3,5), C(-1,0,2) be three... | Mathematics | TestHub
- The shortest distance from the plane 12 x+... | Mathematics | TestHub
- Statement 1 - The distance of the point of... | Mathematics | TestHub
- Statement 1 - L_{1}: \frac{x+1}{3}=\frac{y... | Mathematics | TestHub
- Consider plane P: x+y+z=3 and circle x^{2}... | Mathematics | TestHub
- The distance between the plane x-2 y+z-6=0... | Mathematics | TestHub
- Intersection of a sphere by a plane is cal... | Mathematics | TestHub
- Statement 1 - Let A, B, C be points with p... | Mathematics | TestHub
- If the perpendicular distance of a point P... | Mathematics | TestHub
- In tetrahedron L M N O , edges M L, M N, M... | Mathematics | TestHub
- The equation of the plane through (1,2,3)... | Mathematics | TestHub
- Find the distance of the point \hat{i}+2 \... | Mathematics | TestHub
- Intersection of a sphere by a plane is cal... | Mathematics | TestHub
- If P_{1}, P_{2}, P_{3} denote the distance... | Mathematics | TestHub
- Statement 1 - If x, y, z \in R and 3 x+4 y... | Mathematics | TestHub
- Let A=(0,0,0), B=(1,1,1) , plane P: x-y+z=... | Mathematics | TestHub
- Let P(\alpha, \beta, \gamma) is a variable... | Mathematics | TestHub
- Intersection of a sphere by a plane is cal... | Mathematics | TestHub
Plane (Equations)(26)
- Match the following properties/values rela... | Mathematics | TestHub
- If a plane meets the coordinate axes at an... | Mathematics | TestHub
- If is one end of a diameter of the sphere... | Mathematics | TestHub
- If a plane passing through the point and i... | Mathematics | TestHub
- A variable plane remains at constant dista... | Mathematics | TestHub
- The distance of the point from the plane m... | Mathematics | TestHub
- The equation of the plane which bisects th... | Mathematics | TestHub
- The equation of the right bisector plane o... | Mathematics | TestHub
- If the distance between the planes and can... | Mathematics | TestHub
- Match the following.List-IList-II(A) The d... | Mathematics | TestHub
- Statement 1 - The line \frac{x-1}{3}=\frac... | Mathematics | TestHub
- A variable plane cuts the x-axis, y-axis a... | Mathematics | TestHub
- The equations of three planes are x-2 y+z=... | Mathematics | TestHub
- The plane \frac{x}{a}+\frac{y}{b}+\frac{z}... | Mathematics | TestHub
- Consider plane P: x+y+z=3 and circle x^{2}... | Mathematics | TestHub
- Two lines whose equations are \frac{x-3}{2... | Mathematics | TestHub
- Statement 1 - P is a point (a, b, c) . Let... | Mathematics | TestHub
- Statement 1 - If the planes x=c y+b z, y=a... | Mathematics | TestHub
- Consider the planes P_{1}: 2 x+y+z+4=0, P_... | Mathematics | TestHub
- Plane \Pi contains L_{1}: y / b+z / c=1, x... | Mathematics | TestHub
- A plane passing through (1,1,1) cuts the p... | Mathematics | TestHub
- The plane passing through the point (-2, -... | Mathematics | TestHub
- Match the following.List-IList-II(A) The v... | Mathematics | TestHub
- A plane through P=(0,1,-1) contains line L... | Mathematics | TestHub
- Consider a pyramid O P Q R S located in th... | Mathematics | TestHub
- Match the following pair of planes with th... | Mathematics | TestHub
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