Warm up 1.) (3, 2, -4), (-1, 0, -7) Find the vector in standard position and find the magnitude of the vector.

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Warm up 1.) (3, 2, -4), (-1, 0, -7) Find the vector in standard position and find the magnitude of the vector.

8.4: Perpendicular Vectors

Inner Product of Vectors in a Plane If a and b are 2 vectors (a1, a2), (b1, b2): Then the inner product of a and b is defined as: a ● b = a1∙b1 + a2∙b2 This is also called the dot product Two vectors are perpendicular iff the dot product = 0 Examples: a= (3, 12), b = (8, -2) c = (3, -2) 1.) a ● b 2.) b ● c

Inner product of vectors in space If a and b are 2 vectors (a1, a2,a3) (b1, b2, b3): Then the inner product of a and b is defined as: a ● b = a1∙b1 + a2∙b2 + a3∙b3 Examples: a= (3, 12, 5), b = (8, -2, -4) 1.) a ● b

Cross Product Given a = (a1, a2, a3) and b = (b1, b2, b3) then: Then the cross product a x b is given by: Example: a = (5, 2, 3), b = (-2, 5, 0)