Vector Algebra ...

Let $$\hat{a} \space and \space \hat{b}$$ be mutually perpendicular unit vectors. Then for any arbitrary $$\vec{r}$$.

The vector with initial point $$P(2,-3,5)$$ and terminal point $$Q(3,-4,7)$$ is

The position vector of the point which divides the join of points with position vectors $$\vec a +\vec b$$ and $$2\vec a-\vec b$$ in the ratio $$1:2$$ is

Let $$ \vec{u}, \vec{v} $$ and $$ \vec{w} $$ be vectors such that $$ \vec{u}+\vec{v}+\vec{w}=0 . $$ If $$ |\vec{u}|=3,|\vec{v}|=4 $$ and $$ |\vec{w}|=5, $$ then $$ \vec{u} \cdot \vec{v}+\vec{v} \cdot \vec{w}+\vec{w} \cdot \vec{u} $$ is

Line $$\overrightarrow{r} = \overrightarrow{a} + \lambda \overrightarrow{b}$$ will not meet the plane $$\overrightarrow{r} \cdot \overrightarrow{n} = q$$, if 

If $$\vec \alpha | =4$$ and $$ -3 \le \lambda \le 2$$, then the range of $$ | \lambda \vec \alpha |$$ is 

If $$\vec a, \vec b, \vec c$$ are unit vector such that $$\vec a +\vec b +\vec c=\vec 0$$, then the value of $$\vec a \vec b+\vec b. \vec c+\vec c. \vec a$$ is 

The vector having initial and terminal points as $$(2, 5, 0)$$ and $$(-3, 7, 4)$$, respectively is 

The projection of vector $$\vec a=2\hat i-\hat j+\hat k$$ along $$\vec b=\hat i+2\hat j+2\hat k$$ is

If $$\vec a, \vec b, \vec c$$ are three vectors such that $$ \vec a +\vec b+ \vec c=\vec 0$$ and $$ | \vec a| =2, | \vec b|=3, | \vec c| =5$$, then value of $$\vec a. \vec b+ \vec b. \vec c+ \vec c. \vec a$$ is