List of top Engineering Mathematics Questions on Vector identities

Consider designing a linear binary classifier \( f(x) = \text{sign}(w^T x + b), x \in \mathbb{R}^2 \) on the following training data: 



Class-2: \( \left\{ \left( \begin{array}{c} 0 \\ 0 \end{array} \right) \right\} \) 

Hard-margin support vector machine (SVM) formulation is solved to obtain \( w \) and \( b \). Which of the following options is/are correct?

If \( \nabla \phi = 2xy^2 \hat{i} + x^2z^2 \hat{j} + 3x^2y^2z^2 \hat{k} \), then \( \phi(x,y,z) \) is:
Let $\phi$ be a scalar field, and $\mathbf{u$ be a vector field. Which of the following identities is true for $\nabla \cdot (\phi \mathbf{u})$?}