Vector Algebra ...

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

Let $$\square PQRS$$ be a quadrilateral. If $$M$$ and $$N$$ are midpoints of the sides $$PQ$$ and $$RS$$ respectively then $$\overline {PS} + \overline {QR} =$$

If $$\vec{a}$$ and $$\vec{b}$$ are the vectors determined by two adjacent sides of regular hexagon, then vector $$EF$$ is

If $$p=\hat {i} + \hat{j}, q=4\hat{k}-\hat{j}$$ and $$r=\hat{i}+\hat{k}$$, then the unit vector in the direction of $$3p+q-2r$$ is

If $$\overrightarrow a$$ and $$\overrightarrow b$$ are unit vectors, then angle between $$\overrightarrow a$$ and $$\overrightarrow b$$ for $$\sqrt 3 \overrightarrow a - \overrightarrow b$$ to be unit vector is

If $$a.b=0$$ and $$a+b$$ makes an angle of $${ 60 }^{ o }$$ with $$b$$, then $$\left| a \right| $$ is equal to

If $$a\cdot b =0$$ and $$a + b$$ makes an angle $$60^o$$ with $$a$$, then

If $$a\times b=c$$, $$b\times c=a$$ and $$a,b,c$$ be the mod of the vectors $$a,b,c$$ respectively, then

If $$\widehat i + \widehat j, \widehat j + \widehat k, \widehat i + \widehat k$$ are the position vectors of the vertices of a $$\Delta ABC$$ taken in order, then $$\angle A$$ is equal to

In the given diagram, if PQ$$=$$A, QR$$=$$B and RS$$=$$C, then PS will be equal to :