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Unformatted text preview: 1.2-Dot Product Deﬁnitions: The dot product of the vectors a and b is given by Dot Product computation formula From the deﬁnition, it follows that the angle between two vectors is given by a and b are orthogonal if and only if Orthogonal complements Scalar and Vector projections Work Examples: Find a · b if a =< 3, 2 > and b = i − 4j Find the angle between a =< 3, 1 > and b =< −2, 4 >. Find x such that a =< x, 1 >⊥ b =< 4 + x, 3 > If a = i + 3j and b =< 4, 1 >, ﬁnd the scalar and vector projection of a onto b A 5 kg block slides down a frictionless ramp 5 meters tall and 12 meters long (horizontally). Find the work done by gravity if the block slides the entire length of the ramp. On Your Own: #5,9,10,13,19,23,27,31,33,35,37,43,47,53,55,57 ...
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