Calculus 3 : Dot Product

Example Questions

Example Question #416 : Vectors And Vector Operations

Solve:      Explanation:

The dot product of two vectors is given by Using this, we get Example Question #417 : Vectors And Vector Operations

Solve:      Explanation:

The dot product of two vectors is given by Using this, we get Example Question #418 : Vectors And Vector Operations

Solve:      Explanation:

The dot product of two vectors is given by  Example Question #419 : Vectors And Vector Operations

Find the dot product of the vectors and      Explanation:

The formula for the dot product is . Using the given vectors, we get .

Example Question #420 : Vectors And Vector Operations

Compute the dot product between and .     Explanation:

The formula for the dot product is . Using the two given vectors and solving, .

Example Question #101 : Dot Product

Solve:      Explanation:

The dot product of two vectors is given by  Example Question #102 : Dot Product

Solve:      Explanation:

The dot product of two vectors is found by adding the product of the corresponding components. (For example, .)

For our vectors, we get Example Question #103 : Dot Product

Solve:      Explanation:

The dot product of two vectors is given by the sum of the products of the corresponding components (for example, ).

So, we get Example Question #104 : Dot Product

Solve:      Explanation:

The dot product of two vectors is given by So, we get We used a Pythagorean trigonometric identity to simplify.

Example Question #105 : Dot Product

Solve:      The dot product of two vectors is given by the sum of the products of the corresponding components (ex. )  