What do cross products mean?

Answer 1

In a problem dealing with ratios, the cross produces are the product of the means, and the product of the extremes. These products are eauakl ro each other.

Ratios can be written different ways. a:b :: c:d

the means are the ones closest together (in the middle) their product is bc

the extremes are ones fartherest apart (rt and left ends) their product is ad

so .... bc = ad

Ratios can also be written as fractions.

a / b = c / d

so bc = ad (same thing)

Ex: if 3/x = 21/9 solve by using cross products

21x = 3(9)

21x = 27

x = 27 / 21

x = 1 and 2/7 or in decimal form 1.286 (rounded)

There is also a cross product of vectors if you are studying them.

If 2 vectors, a and b, are acting at some angle C to each other then their cross product is

a x b = a b sin C , where a is the magnitude of vector a, similarly for b

a x b is read as the cross product of vectors a and b, or just shortened to a cross b