The family of curves whose $x$ and $y$ intercepts of a tangent at any point are respectively double the $x$ and $y$ coordinates of that point is

The vectors $\mathbf{A B}=3 \hat{\mathbf{i}}+4 \hat{\mathbf{k}}$ and $\mathbf{A C}=5 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$ are the sides of a $\triangle A B C$, The length of the median through $A$ is

The volume of the parallelopiped whose co terminous edges are $\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+\hat{\mathbf{j}}$ is

Let $\mathbf{a}$ and $\mathbf{b}$ be two unit vectors and $\theta$ is the angle between them. Then, $\mathbf{a}+\mathbf{b}$ is a unit vector, if