Hey guys! I have a question which is pretty straightforward but I'm not sure how to prove it...

Show that for any vectors a, b, and c, vector v = b(a*c) - c(a*b) is orthogonal (perpendicular) to a

There is this theorem which states that if 3 vectors are coplanar, their triple product is equal to 0

Also, If a, b, and c are coplanar, then b * c will be orthogonal to a, hence their dot product will be equal to 0

That's all I could find and I'm not sure if I just prove it by theorem or if i have to do some arithmetic

Any help would be greatly appreciated!