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Find the reflection of the point \((-3,5,2)\) over the line \(x-3 = \dfrac{y-4}{2} = \dfrac{z-1}{2}\). If the new point is of the form ...

\[ \large \sum_{i=1}^{k} \text{lcm}(i, k) = \ ?\] Let \(k \in \mathbb{N}\), and let its prime factorization be \(\displaystyle k = \prod_{i=1}^{n} p_i ^{a_i}\), where ...

We have a vector field \(\vec{F} : \mathbb{R}^2 \to \mathbb{R}^2\) such that \(\vec{F}(x,y)=(2x \sin y,x^2 \cos y)\). Let:

\[ \large \sum_{i=1}^{k}\gcd(i,k) = \ ? \] Let's represent \(k \in \mathbb{N}\) with its prime factorization, i.e., \(\displaystyle k=\prod_{i=1}^{n} {p_i}^{a_i}\), where ...

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