Question

Find the distance from C to D if the coordinates are given as C (-3, 2, 1) and D (r = 5, θ = 20°, Φ = -70°).
1. 5.99 unit
2. 9.07 unit
3. 7.90 unit
4. 6.29 unit

Answer 1

Correct Answer - Option 4 : 6.29 unit

Concept:

Conversion of spherical co-ordinate cartesian co-ordinate is given by

x = r sin θ cos ϕ

y = r sin θ sin ϕ

z = r cos θ

Calculation:

c = (-3, 2, 1); D = (r = 5 θ = 20° ϕ = -70°)

D in cartesian co-ordinate will be

x = 5 sin 20 cos (-70°) = 0.58

y = 5 sin 20 sin (-70°) = -1.606

z = 5 cos 20° = 4.698

So D = (0.58, -1.606, 4.698)

distance between two points (x₁, y₁, z₁) to (x₂, y₂, z₂) is given by

\(d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2+\left(z_2-z_1\right)^2}\)

\(d_{CD}=\sqrt{(.58+3)^2+(-1.606-2)^2+(4.698-1)^2}\)

d_CD = 6.29 unit