In math terms what does cross products mean?

Answer 1

The meaning depends on the context. I can think of at least three different meanings for cross products.

In solving fractional equations, it means equating the product of the left numerator and the right denominator with the product of the right numerator and the left denominator.

More simply, if a/b = c/d then a*d = b*c where a, b, c and d can be numbers or algebraic expressions.

In the context of multiplying polynomials - particularly binomials - the cross product terms are those involving terms that are not "like" terms.

So, for example, (ax+b)*(cx+d) = abx2 + adx + bcx + bd. abx2 is the product of multiplying the "x-terms" while bd is the product of the constant terms so neither is a cross product term but adx = ax*d and bcx = b*cx involve muliplying unlike terms together and so they are cross products.

In vector algebra, the cross product of two vectors, aand b is a vector whose magnitude (size) is equal to the area of the parallelogram created by the vectors and whose direction is perpendicular to the plane of the two vectors. Whether the cross product vector goes along that perpendicular in one direction or its opposite is given by the right hand rule. Point the index finger of the right hand in the direction of the first vector, the middle finger in the direction of the second. Then the extended thumb points in the direction of the resultant.