Lab exercise #12assignment overviewwe are going to work with overloaded operators and making our own class. we are going to make a 2d vector class. some backgroundso if you don’t remember, here is a little background on two-dimensional vectors. a vector is basically an arrow that has a magnitude (a length) and a direction (an angle with respect to typically the x axis). it usually is represented as an x, y pair, where the origin of the vector is a 0,0 and the head of the vector is at thelisted pair. a vectorv + w v-wv*2here are some of the operations you can perform on a vector.vector addition. if v1 is (x, y) and v2 is (a, b), the v+w is (x+a, y+b), a vectorvector multiplication by a scalar. if v1 is (x, y), the v*n is (x*n, y*n), a vectorvector subtraction v-w is the same as v+(w*-1), a vectorvector multiplication with another vector. there are two possibilities, dot product or cross product. we’ll do dot product. if v=(x, y) and w=(a, b), then v*w = x*a + y*b, a scalar. thus the dot product yields a scalar, not a vectorvector magnitude. the magnitude based on the pythagorean theorem for a v=(x, y) says that the magnitude is sqrt(x**2 + y**2). you might look at math. hypot for this