11.6 Dot Product and Angle between Vectors Do Now Find the unit vector of 3i + 4j.

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Presentation transcript:

11.6 Dot Product and Angle between Vectors Do Now Find the unit vector of 3i + 4j

HW Review

Dot Product The dot product of two vectors of two vectors v = and w = is the scalar defined by:

Properties of the Dot Product

Dot Product and Angle Let θ be the angle between two non zero vectors v and w. Then or

Ex Find the angle between v = and w =

Orthogonal Vectors Two nonzero vectors are called perpendicular or orthogonal if the angle between them is π/2 or if = 0

Ex Determine whether v = is orthogonal to u = or w =

Obtuse Angles The angle between two vectors is obtuse if the dot product is < 0

Ex Determine whether the angles between vector v = and the vectors u = and w = are obtuse

Projection The projection of u along a nonzero v is the vector: OR

Ex Find the projection of u = along v =

Ex Find the decomposition of u = with respect to v =

Closure Find the projection of u = along v = HW: p.658 #