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Home » \[ d = \frac12(u + v)t \] - Get link 4share

\[ d = \frac12(u + v)t \] - Get link 4share

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 rac{dD}{dx} = 10x - 16 = 0 \Rightarrow x = rac{8}{5}.

📌 Then $y = 2\left(rac{8}{5}

📌 ight) + 1 = rac{16}{5} + rac{5}{5} = rac{21}{5}$.

📌 Thus, the closest point is $\left(rac{8}{5}, rac{21}{5}

📌 oxed{\left( \dfrac{8}{5},\ \dfrac{21}{5}

📌 Question: Find the vector $\mathbf{v}$ that satisfies $\mathbf{v} imes \mathbf{a} = \mathbf{b}$, where $\mathbf{a} = \langle 1, 2, 3

📌 angle$ and $\mathbf{b} = \langle 4, 5, 6

📌 Solution: The vector equation $\mathbf{v} imes \mathbf{a} = \mathbf{b}$ has a solution only if $\mathbf{a} \cdot \mathbf{b} = 0$, since the cross product is perpendicular to $\mathbf{a}$.

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بعد ذلك، المسافة من $D$ إلى $B$:
\sqrt{(x-a)^2 + (y-a)^2 + z^2} = a\sqrt{2} \quad \Rightarrow \quad (x-...
بتوسيع وتعويض $x^2 + y^2 + z^2 = 2a^2$:
x^2 - 2ax + a^2 + y^2 - 2ay + a^2 + z^2 = 2a^2 \quad \Rightarrow \quad...
أخيرًا، المسافة من $D$ إلى $C$:
\sqrt{x^2 + (y-a)^2 + (z-a)^2} = a\sqrt{2} \quad \Rightarrow \quad x^2...
x^2 + y^2 - 2ay + a^2 + z^2 - 2az + a^2 = 2a^2 \quad \Rightarrow \quad...
x + y = a \quad \text{و} \quad y + z = a
نعوض $y = a - x$ في $y + z = a$:
a - x + z = a \quad \Rightarrow \quad z = x

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