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Home » \( 64 - 80 + 24 - 4 = 4 - Crosslake

\( 64 - 80 + 24 - 4 = 4 - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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oxed{egin{bmatrix} 1 & 2 \ 3 & -1 \end{bmatrix}}
A science communicator is creating a vector visualization for a YouTub...
\mathbf{v} = egin{bmatrix} a \ b \end{bmatrix}, \quad \mathbf{a} = e...
The 2D cross product is:
\mathbf{v} imes \mathbf{a} = a(-4) - b(3) = -4a - 3b
We set this equal to 5:
-4a - 3b = 5
This is a linear equation in two variables. We can express one variabl...
-3b = 4a + 5 \quad \Rightarrow \quad b = -rac{4a + 5}{3}
Thus, all vectors \(egin{bmatrix} a \ -rac{4a + 5}{3} \end{bmatrix}\...

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Next, use Heron's formula to find the area \( A \) of the triangle:
A = \sqrt{s(s - 13)(s - 14)(s - 15)} = \sqrt{21 \times 8 \times 7 \tim...
A = \sqrt{21 \times 336} = \sqrt{7056} = 84 \, \text{cm}^2
The altitude \( h \) corresponding to a side \( a \) is given by:
h = \frac{2A}{a}
Calculate the altitudes for each side:
For side 13 cm:
h_{13} = \frac{2 \times 84}{13} \approx 12.923 \, \text{cm}
For side 14 cm:
h_{14} = \frac{2 \times 84}{14} = 12 \, \text{cm}

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