Vector Algebra ...

If $$\hat{u}$$ and $$\hat{v}$$ are unit vectors and $$\theta$$ is the acute angle between them , then 2$$\hat{u}$$ 3$$\hat{v}$$ is a unit vector for

Let $$\vec{a}$$ = $$\hat{i}$$  $$\hat{j}$$, $$\vec{b}$$ = $$\hat{j}$$  $$\hat{k}$$, $$\vec{c}$$ = $$\hat{k}$$  $$\hat{i}$$. If $$\vec{d}$$ is a unit vector such that $$\vec{a}.\vec{d}$$ = 0 = $$\left | \vec{b}\vec{c}\vec{d} \right |$$ then $$\vec{d}$$ equals :

Vector $$\vec{  A} $$ and $$\vec{  B} $$ include an angle $$\theta $$ between them. If  $$\vec {  A}+\vec {  B}$$ and $$\vec {  A}-\vec {  B}$$  respectively subtend angles $$\alpha $$ and $$\beta$$ with $$\vec {  A}$$, then $$(\tan { \theta } +\tan { \beta} ) $$ is

If $$a$$,$$b$$ and care three mutually perpendicular vectors, then the projection of the vector $$ \left|\frac{a}{|a|}+m \frac{b}{|b|}+n \frac{(a \times b)}{|a \times b|}\right. $$ along the angle bisector of the vector $$a$$ and $$b$$ is

The value of $$\lambda $$ for $$\left( x,y,z \right) \neq \left( 0,0,0 \right) $$ and $$\left( i+j+3k \right) x+\left( 3i-3j+k \right) y+\left( -4i+5j \right) z=\lambda \left( xi+yj+zk \right) $$ are

The position vector of a point lying on the joining the points whose position vectors are $$\overline i + \overline j -\overline k$$ and $$\overline i - \overline j +\overline k$$ is

If $$\overline { a } =-2\overline { i } +3\overline { j } +4\overline { k } $$ and $$\overline { b } =-2\overline { i } -2\overline { j } +3\overline { k } $$ then $$\overline { a } .\overline { b } $$ is 

If $$\overset { \rightarrow  }{ a } ,\overset { \rightarrow  }{ b } ,\overset { \rightarrow  }{ c } $$ are unit vectors such that $$\overset { \rightarrow  }{ a } +\overset { \rightarrow  }{ b } +\overset { \rightarrow  }{ c } =0$$ then the value of $$\overset { \rightarrow  }{ a. } \overset { \rightarrow  }{ b } +\overset { \rightarrow  }{ b } .\overset { \rightarrow  }{ c } +\overset { \rightarrow  }{ c } .\overset { \rightarrow  }{ a. } $$ is 

Let position vector of the orthocentre of $$\triangle ABC$$ be $$\overrightarrow{r}$$. then, which of the following statement(s) is\are correct (Given position vector of points $$a\hat{i},b\hat{j},c\hat{k}$$ and $$abc=0$$)

If C is the mid point of AB and P is any point outside AB , then