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Problem If a \mathbf{a} a b \mathbf{b} b θ \theta θ ∣ a × b ∣ 2 + ( a ⋅ b ) 2 = ∣ a ∣ 2 ∣ b ∣ 2 |\mathbf{a} \times \mathbf{b}|^2 + (\mathbf{a} \cdot \mathbf{b})^2 = |\mathbf{a}|^2 |\mathbf{b}|^2 ∣ a × b ∣ 2 + ( a ⋅ b ) 2 = ∣ a ∣ 2 ∣ b ∣ 2 ∣ a × b ∣ = ( a ⋅ b ) |\mathbf{a} \times \mathbf{b}| = (\mathbf{a} \cdot \mathbf{b}) ∣ a × b ∣ = ( a ⋅ b ) θ = π / 4 \theta = \pi/4 θ = π /4 a × b = ( a ⋅ b ) n ^ \mathbf{a} \times \mathbf{b} = (\mathbf{a} \cdot \mathbf{b})\hat{\mathbf{n}} a × b = ( a ⋅ b ) n ^ n ^ \hat{\mathbf{n}} n ^ θ = π / 4 \theta = \pi/4 θ = π /4 ∣ a × b ∣ ⋅ ( a + b ) = 0 |\mathbf{a} \times \mathbf{b}| \cdot (\mathbf{a} + \mathbf{b}) = 0 ∣ a × b ∣ ⋅ ( a + b ) = 0 Browse the problem library