Unpacked Content
Knowledge
Students know:
- The formula and alternative formula for dot product.
- The properties of the dot product.
- The formula for the angle between two vectors.
- The relationship between the dot product and orthogonal vectors.
- Projection of a vector onto another vector.
- Vector components of v.
Skills
Students are able to:
- Find the dot product of two vectors.
- Find the angle between two vectors.
- Use the dot product to determine if two vectors are orthogonal.
- Find the projection of a vector onto another vector.
- Express a vector as the sum of two orthogonal vectors.
Understanding
Students understand that:
- The dot product of two vectors is the sum of the products of their horizontal components and their vertical components.
- If ? = ?1? + ?1? and ? = ?2? + ?2?, the dot product of ? and ? is defined by ? ? ? = ?1?2 + ?1?2.
- Alternative Formula for the Dot Product: ? ? ? = ??? ??? cos ?, where ? is the smallest non negative angle between v and w.
- Two vectors are orthogonal when the angle between them is 90o. To show that two vectors are orthogonal, show that their dot product is zero.
- A vector may be expressed as the sum of two orthogonal vectors, called the vector components.
Vocabulary
- dot product
- parallel
- orthogonal
- components
- vector projection
- vector components
- decomposition
