The vector ` vec a\ a n d\ vec b` satisfy the equation `2 vec a+ vec b= vec p\ and vec a+2 vec b= vec q ,\ w h e r e\ vec p= hat i+ hat j\ a n d\ vec q= hat i- vec jdot` If `theta` is the angle between ` vec a\ a n d\ vec b"\ "` , then
a.`costheta=4/5` b. `sintheta=1/(sqrt(2))` c. `costheta=\ -4/5` d. `costheta=-3/5`

Explanation

To solve the problem step by step, we will start from the given equations and work our way through to find the angle \( \theta \) between the vectors \( \vec{a} \) and \( \vec{b} \).

### Step 1: Set up the equations
We are given the following equations:
1. \( 2\vec{a} + \vec{b} = \vec{p} \)
2. \( \vec{a} + 2\vec{b} = \vec{q} \)

Where:
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