If the sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one, then the area (in sq. units) of that triangle is

In $\triangle A B C, A D$ and $B E$ are medians drawn from $A$ and $B$. If $A D=\frac{7}{2}, \angle D A B=\frac{\pi}{8}$ and $\angle A B E=\frac{\pi}{4}$, then the area (in sq. units) of $\triangle A B C$ is

If the radius of the incircle of a triangle with sides $5 k, 6 k$ and $5 k$ is 6 , then the largest angle of that triangle is

If $\mathbf{a , b , c}$ are three independent vectors and there exists a non zero scalar traid $(l, m, n)$ such that $l(3 \mathbf{a}+2 \mathbf{b}+\mathbf{c})+m(2 \mathbf{a}+2 \mathbf{b}+3 \mathbf{c})+n(\mathbf{a}+2 \mathbf{b}+5 \mathbf{c})=\mathbf{0}$, then