NCERT Class 12 Maths
Chapter 11: Three Dimensional Geometry
15 Questions Solved
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry — Exercise 11.2
Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.
Question 1
Show that directions (12,−3,−4)/13, (4,12,3)/13 and (3,−4,12)/13 are mutually orthogonal.
Question 2
Show that the directions of the line through (1,−1,2),(3,4,−2) and the line through (0,3,2),(3,5,6) make a right angle.
Question 3
Show that the line through (4,7,8),(2,3,4) is parallel to that through (−1,−2,1),(1,2,5).
Question 4
Find a line through (1,2,3) parallel to (3,2,−2).
Question 5
Find vector and Cartesian equations through (2,−1,4) with direction (1,2,−1).
Question 6
Find the Cartesian equation through (−2,4,−5) parallel to (x+3)/3=(y−4)/5=(z+8)/6.
Question 7
Write the vector form of (x−5)/3=(y+4)/7=(z−6)/2.
Question 8
Find acute angles between (i) r=(2,−5,1)+t(3,2,6) and r=(7,0,−6)+s(1,2,2); (ii) r=(3,1,−2)+t(1,−1,−2) and r=(2,−1,−56)+s(3,−5,−4).
Question 9
Find acute angles between (i) (x−2)/2=(y−1)/5=(z+3)/(−3) and (x+2)/(−1)=(y−4)/8=(z−5)/4; (ii) x/2=y/2=z and (x−5)/4=(y−2)=(z−3)/8.
Question 10
Find p so that the directions of (1−x)/3=(7y−14)/(2p)=(z−3)/2 and (7−7x)/(3p)=(y−5)=(6−z)/5 are orthogonal.
Question 11
Show that (x−5)/7=(y+2)/(−5)=z and x=y/2=z/3 have orthogonal directions.
Question 12
Find the shortest distance between r=(1,2,1)+t(1,−1,1) and r=(2,−1,−1)+s(2,1,2).
Question 13
Find the shortest distance between (x+1)/7=(y+1)/(−6)=(z+1) and (x−3)=(y−5)/(−2)=(z−7).
Question 14
Find the shortest distance between r=(1,2,3)+t(1,−3,2) and r=(4,5,6)+s(2,3,1).
Question 15
Find the shortest distance between r=(1−t,t−2,3−2t) and r=(s+1,2s−1,−2s−1).