Vector Cross Product Calculator

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A vector is a quantity that has magnitude and direction. A vector’s line is its magnitude and arrowhead tells its direction Vectors like velocity or force, when we find cross product gives us another vector that is right angle to both the vectors.

a x b =  |a| |b| sin(θ)n

Example 1: Find out the cross product of vector a = (2,3, 4) and vector b = (5,6, 7)

Solution 1:  Cx = aybz – azby = 3 x 7 – 4 x 6 = 21 – 24 = -3

Cy = azbx – axbz = 4 x 5 – 2 x 7 = 20 – 14 = 6

Cz = axby – aybx = 2 x 6 – 3 x 5 = -3

The cross product of vector a(2,3, 4) and vector b(5,6, 7) will be vector c(-3,6, -3).

Example 2: Find out the cross product of vector a = (4,5, 1) and vector b = (6,3, 5)

Solution 2:  Cx = aybz – azby = 5 x 5 – 1 x 3 = 25 – 3 = 22

Cy = azbx – axbz = 1 x 6 – 4 x 5 = 6 – 20 = -14

Cz = axby – aybx = 4 x 3 – 5 x 6 = -18

The cross product of vector a(2,3, 4) and vector b(5,6, 7) will be vector c(22,-14, -18).