Vector Algebra ...

Given: $$\vec a$$ and $$\vec b$$ are unit vector, and $$\theta $$ be the angle between them.
Then $$\dfrac{{1 - \vec a.\vec b}}{{1 + \vec a.\vec b}} = $$

Given that P = 12, Q = 5 and R = 13 also $$\vec P + \vec Q = \vec R$$, then the angle between $$\vec P$$ and $$\vec Q$$ will be :

A vector of magnitude 5 and perpendicular to $$\hat i - 2\hat j + \hat k$$ and $$2\hat i + \hat j - 3\hat k$$ is 

The vertices of a triangle are $$A(1,1,2),B(4,3,1)$$ and $$C(2,3,5).$$ A vector representing the internal bisector of the angle $$A$$ id 

A unit vector along the direction $$\hat i + \hat j + \hat k$$ has a magnitude:

Four forces act on a point object. The object will be in equilibrium, if:

The vector that must be added to the vector $$\hat{i}-3\hat{j}+2\hat{k}$$ and $$3\hat{i}+6\hat{j}-7\hat{k}$$ so that the resultant vector is a unit vector along the y-axis is:

If $$\left| {\overrightarrow A  \times \overrightarrow B | = \sqrt 3 \overrightarrow {A.} \overrightarrow B } \right.$$ then the value of $$\left| {\overrightarrow A  + \overrightarrow B } \right|$$ is:

  Which of the following is the unit vector perpendicular to $$ \vec{A} $$ and $$ \vec{B} $$ ?

The vector equation of the plane containing the line $$\vec {r}=(-2\hat {i}-3\hat {j}+4\hat {k})+\lambda(3\hat {i}-2\hat {j}-\hat {k})$$ and the point $$\hat {i}+2\hat {j}+3\hat {k}$$ is: