Vector Algebra ...

If $$\overline {a}. \overline {b}, \overline {c}$$ are unit vectors, then $$|\overline {a} - \overline {b}|^{2} + |\overline {b} - \overline {c}|^{2} + |\overline {c} - \overline {a}|^{2}$$ does not exceed.

If $$\overrightarrow {a}$$, $$\overrightarrow {b}$$ and $$\overrightarrow {c}$$ be three non-zero vectors, non-coplanar and if $$\overrightarrow {d}$$ is such that $$\bar { a } =\dfrac { 1 }{ y } \left( \overrightarrow { b } +\overrightarrow { c } +\overrightarrow { d}  \right) $$ and  where $$x$$ and $$y$$ are non-zero real numbers, then $$\dfrac { 1 }{ xy } \left( \vec { a } +\vec { b } +\vec { c } +\vec { d }  \right) =$$

If the vector $$6\hat { i } -3\hat { j } -6\hat { k } $$ is decomposed into vectors parallel and perpendicular to the vector $$\hat { i } +\hat { j } +\hat { k }$$ then the vectors are :

If $$|\overline {a}| = 3, |\overline {b}| = 4$$ and $$|\overline {a} - \overline {b}| = 5$$ then $$|a + b| =$$

$$\bar { a } ,\bar { c } $$ are unit parallel vectors, $$\left| \bar { b }  \right| =6$$, then $$\bar { b } -3\bar { c } =\lambda \bar { a } $$ if $$\lambda=$$

The value of $$\left(a.i\right)i+\left(a.j\right)j+\left(a.k\right)k$$ in terms of vector $$a$$

If the position vectors of A, B, C, D are $$\vec{a}, \vec{b}. 2\vec{a}+3\vec{b}, \vec{a}-2\vec{b}$$ respectively, then $$\vec{AC}, \vec{DB}, \vec{BA}, \vec{DA}$$ are?

If $$\bar{a}, \bar{b}, \bar{c}$$ are position vectors of the non-collinear points A, B, C respectively, the shortest distance of A and BC is?

What vector must be added to the two vectors $$\hat{i}+2\hat{j}+2\hat{k}$$ and $$2\hat{i}-\hat{j}-\hat{k}$$, so that the resultant may be a unit vector along x-axis

If $$A,B,C,D$$ be any four points and $$E$$ and $$F$$ be the mid-points of $$AC$$ and $$BD$$, respectively, then $$\vec{AB}+\vec{CB}+\vec{CD}+\vec{AD}$$ is equal to