Vector Algebra ...

If $$C$$ is the mid point of $$AB$$ and $$P$$ is any point out side $$AB$$, then

$$ABC$$ is a triangle and $$P$$ is any point on $$BC$$. If $$PQ$$ is the resultant of the vectors $$\vec {AP},\ \vec {PB}$$ and $$\vec{PC}$$ then $$ACQB$$ is

If $$\vec{b}$$ is the vector whose initial point divides the joining $$5\hat{i}$$ and $$5\hat{j}$$ in the ratio $$\lambda :$$ $$1$$ and terminal point is at origin. lf $$|\vec{b}|\leq\sqrt{37}$$, then $$\lambda\in$$.

lf the Vector $$\overline{\mathrm{c}},\ \vec{\mathrm{a}}=\mathrm{x}\hat{\mathrm{i}}+\mathrm{y}\hat{\mathrm{j}}+\mathrm{z}\hat{\mathrm{k}},\ \vec{\mathrm{b}}=\hat{\mathrm{j}}$$ are such that $$\vec{\mathrm{a}},\ \vec{\mathrm{c}},\ \vec{\mathrm{b}}$$ form $$\mathrm{R}.\mathrm{H}.\ \mathrm{S}$$ then $$\vec{\mathrm{c}}=$$

If $$\vec{r}=3\hat{i}+2\hat{j}-5\hat{k},\vec{a}=2\hat{i}-\hat{j}+\hat{k}$$, $$\vec{b}=\hat{i}+3\hat{j}-2\hat{k},\ \vec{c}=-2\hat{i}+\hat{j}-3\hat{k}$$ such that $$\vec{r}=\lambda\vec{a}+\mu\vec{b}+v\vec{c}$$, then $$\mu,\ \displaystyle \frac{\lambda}{2}$$ , $$v$$ are in

$$\overline{a}=x\hat {i}+y\hat {j}+z\hat {k},\ \overline{b}=\hat {j}$$, then the vector $$\overline{c}$$ for which $$\overline{a},\overline{b},\ \overline{c}$$ form a right hand triangle

If $$\vec a=\hat {i}+2\hat {j}-3\hat {k}$$ and $$\vec {b}=2\hat {i}-\hat {j}-\hat {k}$$ then the ratio between the projection of $$\vec b$$ on $$\vec {a}$$ and the projection of $$\vec {a}$$ on $$\vec {b}$$ is

Which of the following is a true statement. 

Given,  $$|\vec {a}|=|\vec {b}|=1$$ and $$|\vec {a}+\vec {b}|=\sqrt{3}$$. If $$\vec {c}$$ be a vector such that $$\vec {c}-\vec {a}-2\vec {b}=3(\vec {a}\times\vec {b})$$ , then $$\vec {c}.\vec {b}$$ is equal to

If the position vector of a point $$A$$ is $$\overrightarrow { a } +\overrightarrow { 2b } $$ and $$\overrightarrow { a }$$ divides $$\overrightarrow{AB}$$ in the ratio $$2:3$$, then the position vector of $$B$$ is