Question

Which among the following is the distributive law for the cross product of three vectors?

(a) Px(Q+S) = (PxQ) + (PxS)

(b) Px(QxS) = (PxQ) + (PxS)

(c) Px(QxS) = (PxQ) x (PxS)

(d) Px(Q+S) = (PxQ) + (QxS)

The question was asked in a national level competition.

The above asked question is from Dot Product and Cross Product in chapter Force Vectors of Engineering Mechanics

Answer 1

The correct option is (a) Px(Q+S) = (PxQ) + (PxS)

The explanation: The distributive law works just like the simple multiplication of the constant before the brackets. That is in the equation Px(Q+S) = (PxQ) + (PxS), P is crossed by Q and S both. This is simple as, if we first add the two vectors and then do the cross product or we first do the cross product and the do the sum.