Class 12 Maths ISC 3-D Board Questions
Here we provide Class 12 maths important notes,board questions and predicted questions with Answers for chapter 3-D. These important notes,board questions and predicted questions are based on ISC board curriculum and correspond to the most recent Class 12 maths syllabus. By practising these Class 12 materials, students will be able to quickly review all of the ideas covered in the chapter and prepare for the Class 12 Board examinations.
2016
Q1
(a) Find the image of the point ( 2, -1, 5) on the line : 
Also find the length of perpendicular from the
point ( 2, -1, 5) on the line
(b) Find the cartesian equation of the plane passing through the line of intersection of the planes :
and intersecting y-axis at (0, 3)
solutions
Also find the length of perpendicular from the
point ( 2, -1, 5) on the line(b) Find the cartesian equation of the plane passing through the line of intersection of the planes :
and intersecting y-axis at (0, 3)
solutions
2017
Q2
(a) Show that lines : 
and
intersect. Find the coordinates of their
point of intersection
(b) Find the equation of the plane passing through the point (1,-2, 1) and perpendicular to the line joining the points A(3, 2, 1) and B(1, 4, 2).
solutions
and intersect. Find the coordinates of their
point of intersection(b) Find the equation of the plane passing through the point (1,-2, 1) and perpendicular to the line joining the points A(3, 2, 1) and B(1, 4, 2).
solutions
2018
Q3
The Cartesian equation of a line is: 2x - 3 = 3y + 1 = 5 - 6z. Find the vector equation of a line
passing through (7, -5, 0) and parallel to the given line.
solutions
solutions
2019
Q4
Find the angle between the two lines 2x = 3y = -z and 6x = -y = -4z .
solutions
solutions
Q5
(a) Find the equation of the plane passing through the intersection of the planes 2x + 2y - 3z - 7 =
0 and 2x + 5y + 3z - 9 = 0 such that the intercepts made by the resulting plane on the x-axis and
the z-axis are equal.
(b) Find the equation of the lines passing through the point (2, 1, 3) and perpendicular to the lines
solutions
(b) Find the equation of the lines passing through the point (2, 1, 3) and perpendicular to the lines
solutions
2020
Q6
(a) Find the angles between two lines :
and
(b) Find the equation of the plane passing through the point (2, -3, 1) and perpendicular to the line joining the points (4, 5, 0) and (1, -2, 4).
solutions
and (b) Find the equation of the plane passing through the point (2, -3, 1) and perpendicular to the line joining the points (4, 5, 0) and (1, -2, 4).
solutions
Q7
(a) Find the image of the point (3,-2, 1) in the plane 3x - y + 4z = 2
OR
(b) Determine the equation of the line passing through the point (-1, 3, -2) and perpendicular to the lines:
and 
solutions
(b) Determine the equation of the line passing through the point (-1, 3, -2) and perpendicular to the lines:
and
solutions
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