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NCERT Textbook: Three Dimensional Geometry | Mathematics (Maths) Class 12 - JEE PDF Download

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FAQs on NCERT Textbook: Three Dimensional Geometry - Mathematics (Maths) Class 12 - JEE

1. How is three-dimensional geometry different from two-dimensional geometry?
Ans. Three-dimensional geometry deals with objects that have length, width, and height, whereas two-dimensional geometry only deals with objects that have length and width. In three-dimensional geometry, we work with three coordinates (x, y, and z), while in two-dimensional geometry, we work with two coordinates (x and y).
2. What are the basic elements of three-dimensional geometry?
Ans. The basic elements of three-dimensional geometry are points, lines, and planes. A point represents a specific location in space, a line is a straight path that extends infinitely in both directions, and a plane is a flat surface that extends infinitely in all directions.
3. How can we calculate the distance between two points in three-dimensional space?
Ans. The distance between two points A(x1, y1, z1) and B(x2, y2, z2) in three-dimensional space can be calculated using the distance formula: Distance = √((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2) This formula is derived from the Pythagorean theorem, which applies to three dimensions.
4. What is the equation of a line in three-dimensional space?
Ans. The equation of a line in three-dimensional space can be expressed in vector form as: r = a + tb where r is a position vector on the line, a is a known vector that represents a point on the line, b is a direction vector that determines the direction of the line, and t is a parameter that can take any real value.
5. How do we determine whether two lines in three-dimensional space are parallel, perpendicular, or neither?
Ans. Two lines in three-dimensional space are parallel if their direction vectors are proportional. In other words, if the direction vectors of the lines, b1 and b2, are multiples of each other, then the lines are parallel. Two lines are perpendicular if the dot product of their direction vectors is zero. If the dot product of b1 and b2 is zero, then the lines are perpendicular. If the direction vectors are neither proportional nor produce a dot product of zero, then the lines are neither parallel nor perpendicular.
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