Question

a square is there of side 2a, a vector from centre is pointing at an angle to one of its side n reflects back to a corner of same side. find these two vectors.

Answer 1

a square is there of side 2a, a vector from centre is pointing at an angle to one of its side, n reflects back to a corner of same side. Find these two vectors.

Solution:

We can introduce the X and Y-axis, which start from the center of the square.

Vector $\vec{a}$ :

$$x _ {a} = a; y _ {a} = \frac {a}{\tan \alpha}; | \vec {a} | = \sqrt {a ^ {2} + \left(\frac {a}{\tan \alpha}\right) ^ {2}} = a \sqrt {1 + \frac {1}{\tan \alpha}}$$ $$\vec {a} = \left\{a, \frac {a}{\tan \alpha} \right\}$$

Vector $\vec{n}$ :

$$x _ {n} = 0; y _ {n} = \frac {a}{\tan \alpha} + a = \frac {a (1 + \tan \alpha)}{\tan \alpha}; | \vec {n} | = \frac {a (1 + \tan \alpha)}{\tan \alpha}$$ $$\vec {n} = \left\{0, \frac {a (1 + \tan \alpha)}{\tan \alpha} \right\}$$

Answer:

$$\vec {a} = \left\{a, \frac {a}{\tan \alpha} \right\}$$ $$\vec {n} = \left\{0, \frac {a (1 + \tan \alpha)}{\tan \alpha} \right\}$$