Section 9.3 The Dot Product. Goals Introduce the dot product of two vectors and explain its significance to work . Discuss the dot product and perpendicularity . Give properties of the dot product. Introduce projections . Introduction.
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a ∙ b = |a||b| cos(π/3) = 4∙ 6∙ ½ = 12
a ∙ b = |a||b| cos(π/2) = 0
as the next slide illustrates:
a ∙ b = |a||b|
a ∙ b = –|a||b|
(2i + 2j – k)∙ (5i– 4j + 2k) =
2(5) + 2(– 4) + (– 1)(2) = 0,
these vectors are perpendicular.
a ∙ b = 2(5) + 2(– 3) + (– 1)(2) = 0,
the definition of dot product gives