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Physics Lesson 2.5.3 - What is the direction of the vector product obtained by the cross product of two vectors?
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Welcome to our Physics lesson on What is the direction of the vector product obtained by the cross product of two vectors?, this is the third 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.
What is the direction of the vector product obtained by the cross product of two vectors?
It seems as a kind of shortcoming the fact that by formula we can only calculate the magnitude of the vector product obtained by the cross product of two vectors. However, this issue is fixed by applying the "drill rule" (or the screwdriver rule). You may remember that if you have ever turned the screwdriver in the clockwise direction, the screw has moved linearly away from you and when you have tried to remove the screw, you have turned the screwdriver anticlockwise to make the screw move towards you. This is illustrated in the figure below:
The same idea is used to determine the direction of the vector c⃗ which is the cross product vector of a⃗ and b⃗. Thus, if we have to find the direction of c⃗ = a⃗ × b⃗, we start rotating from a⃗ to b⃗ (in our example this direction is anticlockwise). Therefore, (like in the screw) the direction of the vector c⃗ will be upwards as shown in the figure.
On the other hand, if we have to find the cross product d⃗ = b⃗ × a⃗ we must start rotating from b⃗ to a⃗. In our example, such direction is clockwise and based on the screwdriver rule, the direction of the vector d⃗ will be downwards. Look at the figure:
From the two above figures, it is obvious that the vectors c⃗ and d⃗ are opposite. Hence, we can write
Or
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