Vector Algebra ...

$$P, Q, R, S$$ have position vectors $$p, q, r, s$$, such that $$\displaystyle p-q=2\left ( s-r \right )$$, then

OABC is a tetrahedron express the vectors $$\displaystyle \overrightarrow{BC},\overrightarrow{CA},\:and\:\overrightarrow{AB}$$ in terms of the vectors $$\displaystyle \overrightarrow{OA},\overrightarrow{OB}\:and\:\overrightarrow{OC}$$

If $$A\left( \overrightarrow { a }  \right) ,B( \overrightarrow { b } ) ,C\left( \overrightarrow { c }  \right) $$ be the vertices of a triangle whose circumcentre is the origin, then orthocenter is given by

If a, b, c are position vectors of the vertices of a $$\displaystyle \Delta ABC,$$ then $$ \displaystyle \overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CA}=$$

Which of the following statements are correct:
If in triangle OAC, B is the mid-point of AC and $$\displaystyle \overrightarrow{OA}= \vec{a}\:$$ and $$\:\overrightarrow{OB}= \vec{b}$$ then

If c is the middle point of AB and P is any point outside AB then

ABCD is a parallelogram and AC, BD are its diagonals Express $$\displaystyle \overrightarrow{AC}\:and\:\overrightarrow{BD}$$ in terms of $$\displaystyle \overrightarrow{AB}\:and\:\overrightarrow{AD}$$ only

If $$\displaystyle \left ( \bar A+\bar B \right )$$ is perpendicular to$$\bar B$$ and If $$\displaystyle \left ( \bar A+2\bar B \right )$$ is perpendicular to $$\bar A$$, then