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Math Assignment Class XII Ch11: 3Dimensional Geometry
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Math. Assignment Class XII Chapter 11
Question 1: A line makes angle 𝜶, 𝛃, 𝛾 with xaxis, yaxis, zaxis. Then find cos2𝜶, cos2𝛃, cos2𝛾 ? Ans. 1 1 
Question 2:
Write vector
equation of the line: 
Question 3: Find the Cartesian equation of the line which passes through the point (2, 4, 5) and is parallel to the line Hint: Two parallel lines have same direction ratio. Ans. 3 
Question 4: Find angle between pair of lines and
Ans 4: 90^{o} 
Question 5: Find the point on the given line at
a distance 3√2 from the point (1, 2, 3). Ans 5: and the point is either

Question 6: Find the length and foot of perpendicular drawn from the point (2, 1, 5) on the line Ans 6: 
Question 7: Find the shortest distance between the lines : Ans 7: 
Question 8: Find the equation of a line passing through the point P(2,1,3) and perpendicular to the lines: and Ans 8: 
Question 9: Show that the following lines are intersecting, also find their point of intersection.
Ans 9: (1, 6, 12) 
Question 10: Show that the following lines are coplanar. 
Question 11: Find the distance of the given plane from the origin: Ans 11 : 2/7 
Question 12: Find the angle between the planes Ans 12 
Question 13:
Find the equation of
the plane which is perpendicular to the plane 5x + 3y + 6z + 8 = 0 and which
contains the line of intersection of planes x + 2y + 3z  4 = 0 and 2x + y 
z + 5 = 0 Ans 13: 51x + 15y  50z + 173 = 0 , λ = 29/7 
Question 14:
Find the equation of
the plane passing through the point (1, 3, 2) and perpendicular to each of
the plane x + 2y + 3z = 5 and 3x + 3y + z = 0. Ans 14: 7x  8y + 3z + 25 = 0 
Question 15:
Find the equation of
the plane through (2, 1, 1) and (1, 3, 4) and perpendicular to the
plane x 2y + 4z = 10. Ans 15: 18x + 17y + 4z 49 = 0 
Question 16: Find image p' of point p having position vector in the plane and also find PP' Ans. 16: Image (3, 5, 2), Length = 2√6 
Question 17: Find the distance of the point (1, 2, 3) from the plane x  y + z = 5 measured parallel to the line Ans 17: λ = 1/7, AB = 1 
Question 18: Find the distance of the point (2, 3, 4) from the given line measured ∥ to the plane 4x + 12y  3z + 1 = 0 Ans 18: λ = 2/3 , Point is (4, 5/2, 2), Distance = 17/2 
Question 19: Find the equation of the plane passing through the point P(4, 6, 2) and the point of intersection of the plane x + y  z = 8 and the line Ans 19 
Question 20: Find the vector equation of the plane through the line of intersection of planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x  y + z = 0. Hence find whether plane thus obtained contains the line Ans 20 : Yes 
Question 21: Find the angle between the following line and plane : and plane Ans 21: 0^{o} 
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