NCERT Class 12 Maths
Chapter 11: Three Dimensional Geometry
5 Questions Solved
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry — Miscellaneous Exercise
Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.
Question 1
Find the angle between nonzero directions (a,b,c) and (b−c,c−a,a−b). Assume a,b,c are not all equal, so both define lines.
Question 2
Find a line parallel to the x-axis and passing through the origin.
Question 3
Find k so directions of (x−1)/(−3)=(y−2)/(2k)=(z−3)/2 and (x−1)/(3k)=(y−1)=(z−6)/(−5) are orthogonal.
Question 4
Find the shortest distance between r=(6,2,2)+t(1,−2,2) and r=(−4,0,−1)+s(3,−2,−2).
Question 5
Find the vector line through (1,2,−4) whose direction is orthogonal to (x−8)/3=(y+19)/(−16)=(z−10)/7 and (x−15)/3=(y−29)/8=(z−5)/(−5).