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3D Vector Calculator
3D Vector Calculator
Dot, cross, magnitude, and angle for 3D vectors
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Vector a
x
y
z
Vector b
x
y
z
a = (1, 2, 3), b = (4, 5, 6) | a · b = aₓbₓ + a_yb_y + a_zb_z, cos θ = (a · b) / (|a| |b|)
Dot product (a · b)
32
Cross product (a × b)
(-3, 6, -3)
Magnitude |a|
3.7417
Magnitude |b|
8.775
Cross magnitude |a × b|
7.3485
Angle between a and b
12.9332 degrees
(0.225726 radians)
Relationship
Oblique
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3D Vector Calculator
Isometric 3D plot showing vector a, vector b from the origin, the cross product a × b perpendicular to both, and the angle between a and b.
x
y
z
a
b
a × b
θ = 12.93°