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# Three Dimensional Geometry

At Saralstudy, we are providing you with the solution of Class 12th mathematics Three Dimensional Geometry according to the latest NCERT (CBSE) Book guidelines prepared by expert teachers. Here we are trying to give you a detailed answer to the questions of the entire topic of this chapter so that you can get more marks in your examinations by preparing the answers based on this lesson. We are trying our best to give you detailed answers to all the questions of all the topics of Class 12th mathematics Three Dimensional Geometry so that you can prepare for the exam according to your own pace and your speed.

In the previous class, we studied the introduction of 3d geometry. Now, we will go in depth of its concepts. This chapter consists of direction cosines and direction ratios of a line joining two points, coplanar and skew lines cartesian and vector equation of a line, shortest distance between two lines, cartesian and vector equation of a plane, angle between two lines; two planes; a line and a plane, distance of a point from a plane.

Download pdf of NCERT Solutions for Class mathematics Chapter 11 Three Dimensional Geometry

Download pdf of NCERT Examplar with Solutions for Class mathematics Chapter 11 Three Dimensional Geometry ### Exercise 1

•  Q1 If a line makes angles 90°, 135°, 45° with x, y and z-axes respectively, find its direction cosines. Q2 Find the direction cosines of a line which makes equal angles with the coordinate axes. Q3 If a line has the direction ratios −18, 12, −4, then what are its direction cosines? Q4 Show that the points (2, 3, 4), (−1, −2, 1), (5, 8, 7) are collinear. Q5 The vertices of ΔABC are A (3, 5, −4), B (−1, 1, 2), and C (−5, −5, −2).

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