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