Porisma

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Expand dot products using magnitudes and an angle

Given ∣a∣=4|\mathbf a|=4, ∣b∣=5|\mathbf b|=5 and the angle between a\mathbf a and b\mathbf b is 45∘45^\circ, find the exact values of the following:

(i) a⋅b\mathbf a\cdot\mathbf b

(ii) (4a+2b)⋅(3a−b)(4\mathbf a+2\mathbf b)\cdot(3\mathbf a-\mathbf b)

(iii) ∣a−b∣2|\mathbf a-\mathbf b|^2

CJC · Discussion · Question 5

Replace a·a by |a|² and use symmetry a·b=b·a.

Read the worked solution