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Three-Dimensional Geometry Class 11 Notes Maths Chapter 11

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FAQs on Three-Dimensional Geometry Class 11 Notes Maths Chapter 11

1. What are the basic concepts of three-dimensional geometry in JEE?
Ans. The basic concepts of three-dimensional geometry in JEE include coordinates in space, distance between two points, section formula, direction cosines, direction ratios, and the equation of a line in 3D.
2. How do you find the distance between two points in three-dimensional space?
Ans. The distance between two points (x1, y1, z1) and (x2, y2, z2) in three-dimensional space can be found using the formula: Distance = √((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)
3. What is the section formula in three-dimensional geometry?
Ans. The section formula in three-dimensional geometry helps in finding the coordinates of a point that divides a line segment joining two given points in a given ratio. The formula is: (x, y, z) = (m*x2 + n*x1)/(m + n), (m*y2 + n*y1)/(m + n), (m*z2 + n*z1)/(m + n) where (x1, y1, z1) and (x2, y2, z2) are the coordinates of the given points, and m and n are the ratios in which the line segment is divided.
4. What are the direction cosines and direction ratios of a line in three-dimensional space?
Ans. Direction cosines of a line in three-dimensional space are the cosines of the angles made by the line with the x, y, and z-axes. Direction ratios of a line are the ratios of the differences of the coordinates of any two points on the line. For a line with direction cosines (l, m, n), the direction ratios are (1/l, 1/m, 1/n).
5. How do you find the equation of a line in three-dimensional space?
Ans. The equation of a line in three-dimensional space can be found using the vector form or the Cartesian form. In the vector form, the equation is given as r = a + λb, where r is the position vector of any point on the line, a is the position vector of a known point on the line, λ is a scalar parameter, and b is the direction vector of the line. In the Cartesian form, the equation is given as (x - x1)/a = (y - y1)/b = (z - z1)/c, where (x1, y1, z1) is a known point on the line and a, b, and c are the direction ratios of the line.
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