If $y = e^{-mx}$ is a solution of the differential equation $\dfrac{d^2y}{dx^2} + 4\dfrac{dy}{dx} + 3y = 0$, then the values of $m$ are

For the differential equation $(x^2 + y^2)\,dy = xy\,dx$, it is given that $y(1) = 1$ and $y(x_0) = e$, then the value of $x_0$ is _____

In $\triangle OAB$, $O(0,0,0),\ A(6,2,-3)$ and $B(4,0,3)$ are the vertices. Let $\vec{a}$ and $\vec{b}$ be position vectors of points $A$ and $B$ respectively and $OM$ is the projection of $\vec{a}$ on $\vec{b}$ then $l(AM)$ is equal to...

Let $\vec{a} = 2\hat{i} - 3\hat{j} + \hat{k},\ \vec{b} = 3\hat{i} + 2\hat{j} + 2\hat{k},\ \vec{c} = 4\hat{i} - 3\hat{j} + \hat{k}$, then the vectors $\vec{a},\ \vec{b},\ \vec{c}$ are