The magnitudes of mutually perpendicular forces $a, b$ and $c$ are $2, 10$ and $11$ respectively. Then the magnitude of its resultant is

If the position vectors of the vertices $A, B, C$ of a triangle $ABC$ are $7j + 10k$,$-i + 6j + 6k$,and $-4i + 9j + 6k$ respectively,then the triangle 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

Given $p = 2a - 3b$,$q = a - 2b + c$,and $r = -3a + b + 2c$,where $a, b,$ and $c$ are non-zero,non-coplanar vectors,then the vector $-2a + 3b - c$ is equal to:

If $a, b$ and $c$ are three non-collinear points and $ka + 2b + 3c$ is a point in the plane of $a, b$ and $c$, then $k =$

Let $A$ be the set of vectors $a = (a_1, a_2, a_3)$ satisfying $\left(\sum_{i=1}^3 \frac{a_i}{2^i}\right)^2 = \sum_{i=1}^3 \frac{a_i^2}{2^i}$. Then,