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Home » Substitute \( y = -\frac43x + \frac103 \): - Get link 4share

Substitute \( y = -\frac43x + \frac103 \): - Get link 4share

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 angle$, find the scalar $k$ such that the vector $\mathbf{p} + k\mathbf{q}$ is perpendicular to $\mathbf{r}$.

📌 Solution: To find $k$ such that $\mathbf{p} + k\mathbf{q}$ is perpendicular to $\mathbf{r}$, we use the dot product condition:

📌 Compute $\mathbf{p} + k\mathbf{q}$:

📌 \mathbf{p} + k\mathbf{q} = \langle 2 - 4k, -1 + 5k, 3 + k

📌 Now compute the dot product with $\mathbf{r} = \langle 1, 2, -2

📌 + 4k = 0 \Rightarrow k = rac{3}{2}

📌 oxed{rac{3}{2}}

📌 Question: A palynologist models pollen distribution across a region using vectors. Given that $\mathbf{u} = \langle 3, -2, 1

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