Let θ be the angle between two unit vectors $\rm \vec a\ and\ \vec b. \ if\ \vec a+2\vec b$ is perpendicular to $\rm 5\vec a-4\vec b$ then what is cos θ + cos 2θ equal to?

Let ABCDEF be a regular hexagon. If $\rm \vec{AD}=m \vec {BC}\ and\ \vec {CF}=n\vec {AB}$ then what is mn equal to 

The vectors $\rm \vec a, \vec b\ and\ \vec c$ are of the same length. If taken pairwise they form equal angles. If $\rm \vec a=̂ i+̂ j\ and \ \vec b=̂ j+̂ k,$ then what can $\vec c$ be equal to? 

I. î + k̂ 

II. $\rm \frac{-\hat i+4\hat j-\hat k}{3}$

Select the correct answer using the code given below. 

The diagonals of a quadrilateral ABCD are along the lines x - 2y = 1 and 4x + 2y = 3. The quadrilateral ABCD may be a