Vector Algebra ...

If $$\vec{a} = (2, 1, -1), \vec{b} = (1,-1,0), \vec{c} = (5, -1, 1) $$ , then what is the unit vector parallel to $$ \vec{a} + \vec{b} - \vec{c} $$ in the opposite direction ?

The position vectors of the points $$A$$ and $$B$$ are respectively $$3\hat { i } -5\hat { j } +2\hat { k } $$ and $$\hat { i } +\hat { j } -\hat { k } $$. What is the length of $$AB$$?

The unit vector perpendicular to the vector $$\hat{i}-\hat{j}$$ and $$\hat{i}+\hat{j}$$ forming a right handed system, is 

Point $$(4, 0)$$ lies on ________.

If the points $$A$$ and $$B$$ are $$\left( 1,2,-1 \right)$$ and $$ \left( 2,1,-1 \right)$$ respectively, then $$ \vec { AB } $$ is

If $$\vec {a} . \hat {i} = \vec {a} . (\hat {i} + \hat {j}) = \vec {a} (\hat {i} + \hat {j} + \hat {k})$$, thus $$\vec {a}=$$

The Polygon Law of Vector Addition is simply an extension of ____________. 

If for unit vectors $$\bar{a}$$ and $$\bar{b}$$, $$\bar{a}+2\bar{b}$$ and $$5\bar{a}-4\bar{b}$$ are each-other, then $$(\bar{a} \wedge \bar{b})=$$ _____________.

The number of vectors of unit length perpendicular to vectors $$\bar{a} = ( 1, 1, 0)$$ & $$\bar{b}= (0, 1, 1)$$ is :

For $$A(1, -2, 4), B(5, -1, 7), C(3, 6, -2), D(4, 5, -1)$$, the projection of $$\overline {AB}$$ on $$\overline {CD}$$ is ________.