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Class 12
Maths :-NCERT Solutions - Three Dimensional Geometry

Page No 477:
Question 6:
Find the Cartesian equation of the line which passes through the point
(−2, 4, −5) and parallel to the line given by


Page No 478:
Question 10:
Find the angle between the following pairs of lines:
(i) 

(ii) and


Page No 478:
Question 11:
Find the angle between the following pairs of lines:
(i) 
(ii) 


Page No 478:
Question 14:
Find the shortest distance between the lines


Page No 478:
Question 15:
Find the shortest distance between the lines  and 


Page No 478:
Question 16:
Find the shortest distance between the lines whose vector equations are


Page No 493:
Question 3:
Find the Cartesian equation of the following planes:
(a)  (b) 
(c) 


Page No 493:
Question 7:
Find the intercepts cut off by the plane


Page No 493:
Question 9:
Find the equation of the plane through the intersection of the planes  and  and the point (2, 2, 1)


Page No 493:
Question 10:
Find the vector equation of the plane passing through the intersection of the planes  and through the point (2, 1, 3)


Page No 493:
Question 11:
Find the equation of the plane through the line of intersection of the planes and which is perpendicular to the plane 


Page No 498:
Question 7:
Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane


Page No 498:

Question 8:
Find the equation of the plane passing through (abc) and parallel to the plane 


Page No 498:
Question 10:
Find the coordinates of the point where the line through (5, 1, 6) and
(3, 4, 1) crosses the YZ-plane


Page No 498:
Question 17:
Find the equation of the plane which contains the line of intersection of the planes  and which is perpendicular to the plane 


Page No 499:
Question 20:
Find the vector equation of the line passing through the point (1, 2, − 4) and perpendicular to the two lines: 


Page No 499:
Question 21:
Prove that if a plane has the intercepts abc and is at a distance of P units from the origin, then