If $\vec{a}, \vec{b}, \vec{c}$ are three vectors such that $|\vec{a}|=3, |\vec{b}|=5, |\vec{c}|=7$,then $|\vec{a}-\vec{b}|^2+|\vec{b}-\vec{c}|^2+|\vec{c}-\vec{a}|^2$ does not exceed:

Write two different vectors having the same direction.

The two vectors $\hat{i}+\hat{j}+\hat{k}$ and $\hat{i}+3\hat{j}+5\hat{k}$ represent the two sides $\vec{AB}$ and $\vec{AC}$ respectively of a $\triangle ABC$. The length of the median through $A$ is

If $\vec{a}, \vec{b}, \vec{c}$ are the position vectors of points $A, B, C$ respectively,and $D$ is the midpoint of $BC$,then $\vec{AD} = \dots$

Let the position vectors of the vertices $A, B$ and $C$ of a triangle be $2 \hat{i}+2 \hat{j}+\hat{k}$,$\hat{i}+2 \hat{j}+2 \hat{k}$ and $2 \hat{i}+\hat{j}+2 \hat{k}$ respectively. Let $l_1, l_2$ and $l_3$ be the lengths of perpendiculars drawn from the orthocenter of the triangle on the sides $AB, BC$ and $CA$ respectively,then $l_1^2+l_2^2+l_3^2$ equals:

Three forces of magnitudes $1, 2, 3 \text{ dynes}$ meet at a point and act along the diagonals of three adjacent faces of a cube. The resultant force is ............ $\text{dyne}$.