Vector Algebra ...

$$P, Q$$ have position vectors $$\vec {a}$$ & $$\vec {b}$$ relative to the origin '$$O$$' and $$ X, Y$$  divide $$\vec{PQ}$$ intermally and extemally respectively in the ratio $$2:1$$, then vector $$\vec{XY}= $$

If . and $$\times $$ represent dot product and cross product respectively then which of the following is meaningless?

If $$\vec{a}.\vec{b}=0$$ and $$\vec{a}\times \vec{b}=0$$ then

A straight line $$r=a+\lambda b$$ meets the plane $$r.n=0$$ in $$P$$. The position vector of $$P$$ is

$$P$$ is a point on the line through the point $$A$$ whose position vector is $$\overrightarrow{a}$$ and the line is parallel to the vector $$\overrightarrow{b}$$. If $$PA=6$$, the position vector of $$P$$ is

If $$G$$ and $$G'$$ be the centroids of the triangles $$ABC$$ and $$A'B'C'$$ respectively, then $$\overrightarrow { AA' } +\overrightarrow { BB' } +\overrightarrow { CC' } =$$

Five coplanar forces of equal magnitudes $$10 N$$ each, act at a point such that the angle between any two consecutive forces is same. The magnitude of their resultant is :

Let $$\overrightarrow{AB}=3\hat{i}+\hat{j}-\hat{k}$$ and $$\overrightarrow{AC}=\hat{i}-\hat{j}+3\hat{k}$$. If the point $$P$$ on the line segment $$BC$$ is equidistant from $$AB$$ and $$AC$$ then $$\overrightarrow{AP}$$ is

If the vectors $$\vec{a}$$, $$\vec{b}$$, $$\vec{c}$$ and $$\vec{d}$$ are coplanar, then $$\left ( \vec{a}\times \vec{b} \right )\times \left ( \vec{c}\times \vec{d} \right )$$ is equal to

There are $$N$$ co-planar vectors each of magnitude $$V$$. Each vector is inclined to the preceding vector at angle $$2 \pi/N$$. What is the magnitude of their resultant?