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3D Cartesian Coordinate System

Vector: A = A_xa_x + A_ya_y + A_za_z
Differential: dl = dx a_x + dy a_y + dz a_z
Points: P(x,y,z) → P′(x+dx,y+dy,z+dz)

Vector A — Point P (All 8 Octants)

Ax (X)

Ay (Y)

Az (Z)

X axis / a_x

Y axis / a_y

Z axis / a_z

Vector A (O → P)

Vector dl (P → P′)

Dashed lines = projections

Live Coordinates
P ( 3.5, 4.0, 4.5 )
P′ ( 5.0, 5.5, 6.0 )
A |A| = 7.02
dl |dl| = 2.60
dl1 = dx aₓ + dy aᵧ
dl2 = dy aᵧ + dz a𝓏