How do you find the angle between the vectors $v = i + j, w = 2 i - 2 j$ $v=i+j, w=2i-2j$ ?

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Answer 1 · 2017-02-09T09:29:52

The angle is $= 90$ $=90$ º

The angle between $\to v$ $vecv$ and $\to w$ $vecw$ is given by the dot product definition.

$\to v . \to w = ∥ \to v ∥ \cdot ∥ \to w ∥ cos θ$ $vecv.vecw=∥vecv∥*∥vecw∥costheta$

Where $θ$ $theta$ is the angle between $\to v$ $vecv$ and $\to w$ $vecw$

The dot product is

$\to v . \to w = ⟨ 1, 1 ⟩ . ⟨ 2, - 2 ⟩ = 2 - 2 = 0$ $vecv.vecw=〈1,1〉.〈2,-2〉=2-2=0$

The vectors are perpendicular

$θ = 90$ $theta=90$ º

How do you find the angle between the vectors v=i+j,w=2i−2jv=i+j, w=2i-2j?