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Home » Shocking Multiplication Chart 1-12 Unlocked – Make Math Fun & Fast! - AMAZONAWS

Shocking Multiplication Chart 1-12 Unlocked – Make Math Fun & Fast! - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 oxed{egin{bmatrix} 1 & 2 \ 3 & -1 \end{bmatrix}}

📌 A science communicator is creating a vector visualization for a YouTube video and needs to find a vector \(\mathbf{v} = egin{bmatrix} a \ b \end{bmatrix}\) such that \(\mathbf{v} imes \mathbf{a} = 5\), where \(\mathbf{a} = egin{bmatrix} 3 \ -4 \end{bmatrix}\) and cross product in 2D is defined as \(\mathbf{v} imes \mathbf{a} = a_1b_2 - a_2b_1\).

📌 \mathbf{v} = egin{bmatrix} a \ b \end{bmatrix}, \quad \mathbf{a} = egin{bmatrix} 3 \ -4 \end{bmatrix}

📌 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 variable in terms of the other. Solving for \(b\):

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Subtract \(\frac{8}{3}\) from both sides:
4v < 25 - \frac{8}{3} = \frac{75}{3} - \frac{8}{3} = \frac{67}{3}
Now divide by 4:
v < \frac{67}{12} \approx 5.583
Since \( v \) is a positive integer, the largest possible value is \(...
4(5) + \frac{8}{3} = 20 + \frac{8}{3} = \frac{68}{3} \approx 22.67 < 2...
Try \( v = 6 \):
4(6) + \frac{8}{3} = 24 + \frac{8}{3} = \frac{72+8}{3} = \frac{80}{3}...
So \( v = 6 \) exceeds the limit. Thus, the maximum possible integer v...
Question:** What is the greatest common factor of 72 and 108?

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