Vector Algebra ...

If $$\overline{a},\overline{b},\overline{c},$$ are unit vectors such that $$\overline{a}+\overline{b}+\overline{c}+\overline{c.a}=$$

If the scalar projection of the vectors $$xi-j+k$$ on the vector $$2i-j+5k$$ is $$\cfrac { 1 }{ \sqrt { 30 }  } $$, then the value of $$x$$ is equal to 

$$a$$ and $$c$$ are unit vectors and $$|b| = 4$$. If angle between $$b$$ and $$c$$ is $$\cos^{-1}\left (\dfrac {1}{4}\right )$$ and $$a\times b = 2a\times c$$, then $$b= \lambda a + 2c$$, where $$\lambda$$ is equal to

Let $$\vec{OB} =\hat { i } +2\hat { j } +2\hat { k }$$ and $$\vec{OA} =4\hat { i } +2\hat { j } +2\hat { k } $$. The distance of the point $$B$$ from the straight line passing through $$A$$ and parallel to the vector $$2\hat { i } +3\hat { j } +6\hat { k } $$ is

Given that A$$+$$B$$+$$C$$=0$$. Out of three vectors, two are equal in magnitude and the magnitude of third vector is $$\sqrt{2}$$ times that of either of the two having equal magnitude. Then, the angles between the vectors are given by.

Let $$a,b,c$$ be three non-zero vectors such that no two of these are collinear. If the vectors $$a+2b$$ is collinear with $$c$$ and $$b+3c$$ is collinear with $$a$$ ($$\lambda$$ being some non-zero scalar), then $$a+2b+6c$$ equals to

Let $$\vec { a } =\hat { i } +\hat { j } -\hat { k } ,\vec { b } =\hat { i } -\hat { j } +\hat { k } $$ and $$\vec { c } $$ be a unit vector perpendicular to $$\vec { a } $$ and coplanar with $$\vec { a } $$ and $$\vec { b } $$, then $$\vec { c } $$ is

Let $$a, b, c$$ be three non-coplanar vectors and $$r$$ be any arbitrary vector, then the expression $$(\vec {a}\times \vec {b})\times (\vec {r}\times \vec {c}) + (\vec {b} \times \vec {c})\times (\vec {r}\times \vec {a}) + (\vec {c}\times \vec {a}) \times (\vec {r}\times \vec {b})$$ is always equals to

Find $$k$$ if magnitude of vectors joining $$(0,k,0)$$ and $$(1,1,1)$$ is $$\sqrt {11}$$

If three vectors $$ a, b, c $$ satisfy $$ a+b+c=0$$ and $$ |a| = 3, |b| = 5, |c| = 7 , $$ then the angle between $$a$$ and $$b$$ is :