Vector Algebra ...

Let $$ABC$$ be an acute scalene triangle, and $$O$$ and $$H$$ be its circumcentre and orthocentre respectively. Further let $$N$$ be the midpoint of $$OH$$. The value of the vector sum $$\vec {NA} + \vec {NB} + \vec {NC}$$ is

Direction angle of a vector is $$30^{\circ}$$, then find the vector.

In the diagram, vector C is equivalent to.

The position vectors of A, B are a, 6 respectively. The position vector of C is $$\dfrac {5\bar{a}}{3} -\bar{b}$$. Then 3 

If $$\bar{a},\bar{b}, \bar{c}$$ are unit vectors such that $$\bar{a}+ \bar{b}+ \bar{c}=\bar{0}$$, then $$\bar{a}.\bar{b}+ \bar{b}.\bar{c}+ \bar{c}.\bar{a}=$$

If $$\vec { PR } =2\vec { i } +\vec { j } +\vec { k } ,\vec { QS } =-\vec { i } +3\vec { j } +2\vec { k } $$ then the area of the quadrilateral $$PQRS$$ is:

If $$\overline {e} = l\overline {i} + m\overline {j} + n\overline {k}$$ is a unit vector, the maximum value of $$lm + mn + nl$$ is

If $$|\vec {a}| = 3, |\vec {b}| = 4$$ and $$|\vec {a} - \vec {b}| = 7$$ then $$|\vec {a} + \vec {b}| =$$

The projection of the vector $$\hat {i} - 2\hat {j} + \hat {k}$$ on the vector $$4\hat {i} - 4\hat {j} + 7\hat {k}$$ is

$$\overline { a } ,\overline { b } ,\overline { c } $$ are three vectors such that $$\left| \overline { a }  \right| =1,\left| \overline { b }  \right| =2,\left| \overline { c }  \right| =3$$ and $$\overline { b } ,\overline { c } $$ are perpendicular. IF projection of $$\overline { b } $$ on $$\overline { a } $$ is the same as the projection of $$\overline { c } $$ on $$\overline { a } $$, then $$\left| \overline { a } -\overline { b } +\overline { c }  \right| $$