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Home » Subtract 81: \( b^2 = 144 \). - Blask

Subtract 81: \( b^2 = 144 \). - Blask

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 \|\mathbf{v}\| = \sqrt{(-1)^2 + 2^2} = \sqrt{1 + 4} = \sqrt{5}

📌 Now, substitute these into the formula:

📌 = 5 \cdot \sqrt{5} \cdot \cos \theta

📌 Solve for $\cos \theta$:

📌 \cos \theta = \frac{5}{5 \cdot \sqrt{5}} = \frac{1}{\sqrt{5}} = \frac{\sqrt{5}}{5}

📌 \boxed{\frac{\sqrt{5}}{5}}

📌 An astrophysics researcher models the trajectory of a star near a black hole using vectors. If $\mathbf{a} = \begin{pmatrix} 2 \\ -3 \\ 1 \end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix} 1 \\ 4 \\ -2 \end{pmatrix}$, find a vector $\mathbf{c}$ orthogonal to both $\mathbf{a}$ and $\mathbf{b}$.

📌 A vector $\mathbf{c}$ orthogonal to both $\mathbf{a}$ and $\mathbf{b}$ can be found using the cross product:

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