$A$ line segment $PQ$ has the length $63$ and direction ratios $(3, -2, 6)$. If this line makes an obtuse angle with the $X$-axis,then the components of the vector $\vec{PQ}$ are

If $ABCDEFGH$ is a convex octagon,then $\vec{AB} + \vec{BC} + \vec{CD} + \vec{DE} + \vec{AH} + \vec{HG} + \vec{GF} + \vec{FE} = $

Let $\vec{a}=\hat{i}+\hat{j}+\hat{k}$ and $\vec{b}$ be two vectors such that $\vec{a} \cdot \vec{b}=1$, $\cos(\theta) = \frac{1}{3}$ where $\theta$ is the angle between $\vec{a}$ and $\vec{b}$, and the components of $\vec{b}$ with respect to $(\hat{i}, \hat{j}, \hat{k})$ are integers. Then the number of possible vectors that represent $\vec{b}$ is

$A$ vector $r$ is equally inclined with the coordinate axes. If the tip of $r$ is in the positive octant and $|r| = 6$,then $r$ is

If the vectors $\vec{AB} = -3\hat{i} + 4\hat{k}$ and $\vec{AC} = 5\hat{i} - 2\hat{j} + 4\hat{k}$ are the sides of a $\triangle ABC$, then the length of the median through $A$ is

Write two different vectors having the same magnitude.