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Compute the dot product for each of the subsequent equation
(a) v→ = 5i→ - 8j→ , w→ = i→ + 2j→
(b) a→ = (0, 3, -7) , b→ = (2, 3,1)
Solution
(a) v→ • w→ = 5 -16 = -11
(b) a→ • b→ = 0 + 9 = 2
Not much more to do with these other than use the formula.
Sketch several trajectories for the system, x 1 ' = x 1 + 2x 2 x 2 ' = 3x 1 + 2x 2
Properties of Dot Product u → • (v → + w → ) = u → • v → + u → • w → (cv → ) • w → = v → •(cw → ) = c (v → •w → ) v → • w → = w → • v →
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