Vector Algebra ...

$$EFGH$$ is a rhombus such the angle $$EFG$$ is $${60}^{o}$$. The magnitude of vectors $$\overrightarrow { FH } $$ and $$\left\{ m\overrightarrow { EG }  \right\} $$ are equal where $$m$$ is a scalar. What is the value of $$m$$?

The direction cosines l , m and n of two lines are connected by the relations l+m+n=0, lm=0, then the angles between them is 

If the sum of two unit vectors is also a unit vector, then the angle between the two vectors is

If P(x, y, z) is a point on the line segment joining Q(2, 2, 4) and R(3, 5, 6) such that the projections of $$\overrightarrow{OP}$$ on the axes are $$\dfrac{13}{5}, \dfrac{19}{5}, \dfrac{26}{5}$$ respectively, then P divides QR in the ratio

What are coinitial vectors.?

If three non-zero vectors are $$a=a_1i+a_2j+a_3k , \, b=b_1i+b_2j+b_3k$$ and $$ c=c_1i+c_2j+c_3k$$ . If c is the unit vector perpendicular to the vectors a and b the angle between a and b is $$\dfrac{\pi}{6}$$ , then $$\begin{vmatrix}a_1 & a_2 & a_3\\ b_1 & b_2 & b_3 \\ c_1 & c_2 & c_3\end{vmatrix}$$ is equal to

If the vectors $$\overline { c } ,\overline { a } =x\hat { i } +y\hat { j } +z\hat { k } $$, and $$\overline { b } =\hat { j }$$  are such that $$\overline { a } ,\overline { c } \ and \ \overline { b }$$  from a right handed system, then $$\overline { c }$$  is 

Let $$O$$ be an interior point of $$\triangle ABC$$ such that $$\overline {OA} + 2\overline {AB} + 3\overline {OC} = \overline {O}$$, then the ratio of $$\triangle ABC$$ to area of $$\triangle AOC$$ is

If vectors $$i+2j+2k$$ is rotated through an angle of $${90}^{o}$$ so as to cross positive direction of y-axis, then the vector in the new positive is?

A point $$C = \dfrac {5\overline {a} + 4\overline {b} - 5\overline {c}}{3}$$ divides the line joining the points $$A$$ and $$B = 2\overline {a} + 3\overline {b} - 4\overline {c}$$ in the ratio $$2 : 1$$, then the position vector of $$A$$ is