Section 6.2: Dot Product of Vectors

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Presentation transcript:

Section 6.2: Dot Product of Vectors Do Now – (5 min. – no talking first 4!) Find a unit vector starting at the origin and passing through (-3,-4). Find the magnitude and direction angle of the vector 5i – 12j

Find the dot product. Given and ,

Use dot product to find magnitude of a vector.

Use dot product to find the angle b/w vectors.

Orthogonal Vectors The vectors u and v are orthogonal if and only if . Prove that the vectors and are orthagonal. Parallel: angle b/w vectors is 0 or 180. Perpendicular: angle b/w vectors is 90. Otherwise, neither.

Projecting One Vector Onto Another If u and v are nonzero vectors, the projection of u onto v is… Find the vector projection of onto Then, write u as a sum of two orthogonal vectors, one of which is

Application Problem