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Home » where to watch red sox vs detroit tigers - Redraw

where to watch red sox vs detroit tigers - Redraw

📅 May 6, 2026 👤 scraface

May 06, 2026

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📌 Largest integer: \(32 + 4 = 36\)

📌 #### 36Question: A startup is developing a medical device that uses vector-based sensor arrays to detect physiological signals. Suppose two sensor vectors are given as $\vec{v} = \begin{pmatrix} 3 \\ -2 \\ x \end{pmatrix}$ and $\vec{w} = \begin{pmatrix} x \\ 4 \\ -1 \end{pmatrix}$. Find the value of $x$ such that the vectors are orthogonal.

📌 Solution: For two vectors to be orthogonal, their dot product must be zero. Compute the dot product:

📌 \vec{v} \cdot \vec{w} = 3x + (-2)(4) + x(-1) = 3x - 8 - x = 2x - 8

📌 Set the dot product equal to zero:

📌 2x - 8 = 0 \quad \Rightarrow \quad 2x = 8 \quad \Rightarrow \quad x = 4

📌 Thus, the value of $x$ that makes the vectors orthogonal is $\boxed{4}$.

📌 Question: An educator is using a STEM project to teach vector geometry. In a 3D coordinate system, a student plots three vertices of a regular tetrahedron: $A(1, 0, 0)$, $B(0, 1, 0)$, and $C(0, 0, 1)$. Find the integer coordinates of the fourth vertex $D$ such that all edges of the tetrahedron are of equal length.

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