Final answer:
We can write out both sides in component form and compare them. The left side is (A × B) × C and the right side is (B · C)A - (A · C)B.
Step-by-step explanation:
The BAC-CAB rule, also known as the triple vector product, is a mathematical rule used to find the cross product of three vectors. It states that the cross product of the cross product of three vectors A, B, and C is equal to B multiplied by the dot product of A and C, minus C multiplied by the dot product of A and B.
To prove the BAC-CAB rule, we can write out both sides in component form. Starting with the left side, we take the cross product of the cross product: (A × B) × C. Expanding this expression and using the vector identity (A × B) × C = (C · A)B - (C · B)A, we can write out the left side in component form.
On the right side, we have (B · C)A - (A · C)B. Writing this out in component form, we take the dot products of A and C, and B and C, and multiply them by the respective vectors. By comparing the left and right sides in component form, we can see that they are equal, thus proving the BAC-CAB rule.
Learn more about BAC-CAB rule