Vector Algebra ...

If $$2\overrightarrow { a }\cdot \overrightarrow { b } =\left| \overrightarrow { a }  \right| \left| \overrightarrow { b }  \right| $$ then the angle between $$\vec { a }$$ and $$ \vec { b }$$ is 

For non-zero vectors $$\overrightarrow{a}$$ and $$\overrightarrow{b}$$ if $$|\overrightarrow{a}+\overrightarrow{b}| < |\overrightarrow{a}-\overrightarrow{b}|$$, then $$\overrightarrow{a}$$ and $$\overrightarrow{b}$$ are

Let $$\vec {a} = i + 2j + k, \vec {b} = i - j + k$$ and $$\vec {c} = i + j - k$$, a vector in the plane $$\vec {a}$$ and $$\vec {b}$$ whose projection on $$\vec {c}$$ is $$\dfrac {1}{\sqrt {3}}$$ is _____

Point $$P$$ is the endpoint of vector $$OP$$ and point $$Q$$ is the endpoint of vector $$OQ$$ as shown in the above figure. When the vectors $$\overline {OP}$$ and $$\overline {OQ}$$ are added, calculate the length of the resultant vector.

The value of $$x$$ if $$x(\hat { i } +\hat { j } +\hat { k } )$$ is a unit vector is

If $$\displaystyle \vec{a}\:and\:\vec{b}$$ are the vectors $$\displaystyle \overrightarrow{AB}\:and\:\overrightarrow{BC}$$ determined by the adjacent sides of a regular hexagon. What are the vectors determined by the side CD and DE taken in order?

If $$p$$ , $$q$$ and $$r$$ are three non-coplanar vectors such that $$p + q + r  = \alpha s$$ and $$q + r + s = \beta p $$. then $$ p +q +r +s $$  is equal to

$$ABCDEF$$ is a regular hexagon whose centre is $$O$$. The $$\overline { AB } +\overline { AC } +\overline { AD } +\overline { AE } +\overline { AF } $$ is

Two $$\vec a$$ and $$\vec b$$ are at an angle of $$60^o$$ with each other Their resultant makes an angle of $$45^o$$ with $$\vec a$$ If magnitude $$|\vec b|= 2$$ units then $$|\vec a|$$ is:

The magnitude of resultant of three vectors of magnitude $$1,2$$ and $$3$$ whose direction are those of the sides of an equilateral triangle taken in order is: