Physics Lesson 2.5.4 - Cross product of vectors in coordinates

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Welcome to our Physics lesson on Cross product of vectors in coordinates, this is the fourth lesson of our suite of physics lessons covering the topic of Vector Product of Two Vectors, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

Cross product of vectors in coordinates

If the coordinates of the vectors a⃗ and b⃗ (namely xa, ya, za, xb, yb and zb) are given, we can find the coordinates of the vector c⃗ = a⃗ × b⃗ (i.e. xc, yc and zc) using the following formulae:

Example

Three forces are acting on the same object placed at the origin of the coordinates system. The tip of the first force is at (-2, 3, 0) and that of the second force is at (1, 5, -4). What are the coordinates of the tip of the third force vector if these three forces obey the rule of vectors' cross production?

Solution

Before starting the calculation, the position of the two vectors F⃗₁ and F⃗₂ is as shown below

Thus, the direction of the third fore F⃗₃ will be determined by the cross product of the tip's coordinates of the two forces F⃗₁ and F⃗₂. We have

Substituting the known values (F1x = -2, F1y = 3, F1z = 0, F2x = 1, F2y = 5 and F2z = -4), we obtain for the tip's coordinates of F3

Therefore, the tip of vector F3 will be at (-12, -8, -13). This is illustrated in the figure below.

You have reach the end of Physics lesson 2.5.4 Cross product of vectors in coordinates. There are 6 lessons in this physics tutorial covering Vector Product of Two Vectors, you can access all the lessons from this tutorial below.

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