IB DP Maths: AI HL复习笔记3.7.5 The Vector Product

What is the vector (cross) product?

• The vector product (also known as the cross product) is a form in which two vectors can be combined together
• The vector product between two vectors v and w is denoted v × w
• The result of taking the vector product of two vectors is a vector
• The vector product is a vector in a plane that is perpendicular to the two vectors from which it was calculated
  • This could be in either direction, depending on the angle between the two vectors
  • The right-hand rule helps you see which direction the vector product goes in
    • By pointing your index finger and your middle finger in the direction of the two vectors your thumb will automatically go in the direction of the vector product

How do I find the vector (cross) product?

• There are two methods for calculating the vector product
• What properties of the vector product do I need to know?

How do I use the vector product to find the area of a parallelogram?

• The area of the parallelogram with two adjacent sides formed by the vectors vandw is equal to the magnitude of the vector product of two vectors vandwHow do I use the vector product to find the area of a triangle?

• The area of the triangle with two sides formed by the vectors vandw is equal to half of the magnitude of the vector product of two vectors vandw