Each piece of the board has been set up at the midpoint of the respective celland consider that the midpoint of the board to be the origin (0,0). The whitehorse shown at b1 can move to a3 or c3. Naming of the cells is done as (rowposition column position) manner. Hence the white queen is at d1 file. Also theblack king is at e8 file.a) Suppose you are learning the game and you are on the black side. As youdon't know any other moves, you push the knight in g1 file.(i)Express two possible displacement vectors for the knight at g1 file.Find out the unit vectors along these two displacement vectors.(ii)(iii)Find out the direction of these two vectors. (let the angles aremeasured from +x axis in clockwise direction)b) A fianchetto is a special move which provides the quick development ofthe bishop (piece at c1 and fl file). The first move involves pushing thepawn at g2 to g3. Once the pawn moves, the bishop can go to the 2ndrank. Express these two moves (done by the player on the white side) invector form and find the angle between these two vectors. (Note that:Bishop can develop diagonally) 2)An 8x8 chessboard has a square cell which measures f inches on a side.8 罵豆7 &&&&&65328 8 888881 置 A灣鸟鱼買a b c defgh

Given a 8×8 chessboard whose sides of each cell have length β. The chess pieces are placed in the…

Each piece of the board has been set up at the midpoint of the respective cell and consider that the midpoint of the board to be the origin (0,0). The white horse shown at b1 can move to a3 or c3. Naming of the cells is done as (row position column position) manner. Hence the white queen is at dl file. Also the black king is at e8 file. a) Suppose you are learning the game and you are on the black side. As you don't know any other moves, you push the knight in g1 file. (i) Express two possible displacement vectors for the knight at g1 file. (ii) Find out the unit vectors along these two displacement vectors. (iii) Find out the direction of these two vectors. (let the angles are measured from +x axis in clockwise direction)