Vector Algebra ...

If $$\vec {a}$$ and $$\vec {b}$$  are in the plane which is perpendicular to the plane containing $$\vec {c}$$ and $$\vec {d}$$ then $$(\vec {a} \times \vec {b})\times (\vec {c} \times \vec {d})$$ is

If $$\overrightarrow { a } =2\hat { i } +\hat { j } +\hat { k } ,\overrightarrow { b } =3\hat { i } -4\hat { j } +2\hat { k } ,\overrightarrow { c } =\hat { i } -2\hat { j } +2\hat { k } $$ then the projection of $$\overrightarrow { a } +\overrightarrow { b } $$ on $$\overrightarrow { c } $$ is

If $$A(6,3,2),B(5,1,4),C(3,-4,7), D(0,2,5)$$ are four points, then projection of $$CD$$ on $$AB$$ is

If $$\vec a,\vec b$$ and $${\vec c}$$ are unit vectors, then $${\left| {\vec a + \vec b} \right|^2} + {\left| {\vec b - \vec c} \right|^2} + {\left| {\vec c - \vec a} \right|^2}$$ does NOT exceed 

If $$\left| {\vec a} \right| = 2,\left| {\vec b} \right| = 3$$ and  $$\left| {2\vec a - \vec b} \right| = 5,$$ then  $$\left| {2\vec a + \vec b} \right|$$ equals:

If the vectors $$\overrightarrow { a } =\hat { i } -\hat { j } +2\hat { k } ;\overrightarrow { b } =2\hat { i } +4\hat { j } +\hat { k } ;\overrightarrow { c } =\lambda \hat { i } +\hat { j } +\mu \hat { k } $$ are mutually orthogonal, then $$(\lambda,\mu)=$$

If $$\left| \overrightarrow { a }  \right| =3,\left| \overrightarrow { b }  \right| =4$$, if $$\left( \overrightarrow { a } +\lambda \overrightarrow { b }  \right) $$ is perpendicular to $$\left( \overrightarrow { a } -\lambda \overrightarrow { b }  \right) $$ then $$\lambda =$$

The projection of the vector $$2\hat i + \hat j - 3\hat k$$ on  the vector $$\hat i - 2\hat j - \hat k$$

The position vectors of the points A,B,C are $$\overline { i } + 2 \overline { j } - \overline { k } , \overline { i } + \overline { j } + \overline { k } , 2 \overline { i } + 3 \overline { j } + 2 \overline { k }$$ respectively. If A is chosen as the origin then the position vectors of B and C are 

If $$|a|=5.|\vec{b}|=4$$, and $$|c|=3$$. then what will be the value of $$\vec{a}.\vec{b}+\vec{b}.\vec{c}+\vec{c}.\vec{a}$$ given that $$\vec{a}+\vec{b}+\vec{c}=0$$