Chapter 12: Introduction to 3D Geometry

Q1. Find the distance between (1, 2, 3) and (4, 6, 8).

Solution

d = √[(4-1)² + (6-2)² + (8-3)²]
= √(9 + 16 + 25) = √50 = 5√2

Q2. Find the coordinates of the point dividing the join of (1, -2, 3) and (4, 5, -3) in ratio 2:1.

Solution

x = (2×4 + 1×1)/3 = 3
y = (2×5 + 1×(-2))/3 = 8/3
z = (2×(-3) + 1×3)/3 = -1
Point: (3, 8/3, -1)