Vector projections (resolutes)

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Presentation transcript:

Vector projections (resolutes) Scalar resolute (projection) of vector a onto vector b Vector resolute (projection) of vector a onto vector b.

Vector resolutes We want to resolve vector a in two components: one parallel to vector b and one perpendicular to vector b.

Scalar resolute of a onto b Vector a has two components: and so that The length of vector is called the scalar resolute (projection) of a onto b.

Vector resolute of a onto b Vector is the vector resolute of a onto b (or in the direction of b.

Vector resolute of a in the direction perpendicular to b Vector is the vector resolute of a in the direction perpendicular to b.

Example 1 Given two vectors Find: The unit vector in the direction of u b) The scalar resolute of v onto u c) The vector resolute of v in the direction of u d) The vector resolute of v in the direction perpendicular to u

Example 1 continued Scalar resolute Vector resolute

Vector resolute of v in the direction perpendicular to u