Table of Contents
Cross Product of Two Vectors
The cross product of two vectors is a vector that is perpendicular to both of the original vectors. It is calculated by taking the product of the magnitude of the two vectors and the sine of the angle between them.
What is a Vector?
A vector is a mathematical object that has both magnitude and direction. Vectors can be represented as arrows in a two-dimensional plane or as points in a three-dimensional space. Vectors can be added and subtracted, and their components can be multiplied and divided.
Labeling a Vector
There are a few ways to label a vector. One way is to use an arrow notation. In this notation, the vector is written as an equation with an arrow above the equation. The arrow points in the direction of the vector.
Another way to label a vector is to use a coordinate notation. In this notation, the vector is written as a list of numbers. The first number is the x-coordinate and the second number is the y-coordinate.
The Magnitude of the Vector Product
The magnitude of the vector product is the product of the magnitudes of the vectors and the cosine of the angle between them.
Some More Information about Cross Products
The cross product is a vector quantity that is the result of multiplying two vectors together. It is perpendicular to both of the original vectors and is found by taking the vector product of the two vectors. The magnitude of the cross product is the product of the magnitudes of the two vectors and the direction is determined by the right hand rule.
Direction of the Vector Product
The direction of the vector product is perpendicular to both of the vectors that make it up.
Commutative Property of Addition
The commutative property of addition states that for any two numbers a and b, a + b is the same as b + a.
Distributive Property
The distributive property states that for every number A there is a number B such that A + (B x C) = (A + B) x C. In symbols:
For every a there is a b such that a + (b x c) = (a + b) x c.
The Cross Product is Distributive
The Cross Product is distributive over addition and subtraction.
Cross Product of Two Vector Product Formula
The cross product of two vectors is a vector that is perpendicular to both of the original vectors and has a magnitude equal to the product of the magnitudes of the two original vectors.
Find the product of the following using vector product formula: u = 2i + j – 3k ,v = 4j + 5k.
The product of u and v is 108i – 15k.
