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Problem For any non-zero vectors a \mathbf{a} a b \mathbf{b} b θ \theta θ cos θ \cos\theta cos θ a ⋅ b ∣ a ∣ 2 + ∣ b ∣ 2 \dfrac{\mathbf{a}\cdot\mathbf{b}}{|\mathbf{a}|^{2}+|\mathbf{b}|^{2}} ∣ a ∣ 2 + ∣ b ∣ 2 a ⋅ b a ⋅ b ∣ a ∣ ∣ b ∣ \dfrac{\mathbf{a}\cdot\mathbf{b}}{|\mathbf{a}|\,|\mathbf{b}|} ∣ a ∣ ∣ b ∣ a ⋅ b ∣ a ∣ ∣ b ∣ a ⋅ b \dfrac{|\mathbf{a}|\,|\mathbf{b}|}{\mathbf{a}\cdot\mathbf{b}} a ⋅ b ∣ a ∣ ∣ b ∣ ( a ⋅ b ) 2 ( ∣ a ∣ ∣ b ∣ ) 2 \dfrac{(\mathbf{a}\cdot\mathbf{b})^{2}}{(|\mathbf{a}|\,|\mathbf{b}|)^{2}} ( ∣ a ∣ ∣ b ∣ ) 2 ( a ⋅ b ) 2 Browse the problem library