The number of spheres of radius r touching the coordinate axes is

ABCDEFGH is a cuboid with base ABCD. Let A(0, 0, 0), B(12, 0, 0), C(12, 6, 0) and G(12, 6, 4) be the vertices. If α is the angle between AB and AG; β is the angle between AC and AG, then what is the value of cos 2α + cos 2β? 

Let $\rm \vec{a}, \vec{b}$ and $\rm\vec{c}$ be unit vectors such that $\rm\vec{a} \times \vec{b}$ is perpendicular to $\vec{c}$. If θ is the angle between $\rm\vec{a}$ and $\rm\vec{b}$, then which of the following is/are correct?

1. $\rm\vec{a} \times \vec{b} = sin ~\theta~ \vec{c} $

2. $\rm\vec {a} \cdot (\vec{b}\times \vec{c})=0$

Select the correct answer using the code given below.

If $\rm\vec{a}+3\vec{b} = 3\hat{i}- \hat{j}$ and $\rm2\vec{a}+\vec{b} = \hat{i}- 2\hat{j}$, then what is the angle between $\rm\vec{a}$ and $\rm\vec{b}$