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)
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)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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 d1 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.
Find out the unit vectors along these two displacement vectors.
(ii)
(iii)
Find out the direction of these two vectors. (let the angles are
measured from +x axis in clockwise direction)
b) A fianchetto is a special move which provides the quick development of
the bishop (piece at c1 and fl file). The first move involves pushing the
pawn at g2 to g3. Once the pawn moves, the bishop can go to the 2nd
rank. Express these two moves (done by the player on the white side) in
vector form and find the angle between these two vectors. (Note that:
Bishop can develop diagonally)
Transcribed Image Text:2)
An 8x8 chessboard has a square cell which measures f inches on a side.
8 罵豆
7 &&&&&
6
5
3
28 8 88888
1 置 A灣鸟鱼買
a b c defgh
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Transcribed Image Text:b) A fianchetto is a special move which provides the quick development of
the bishop (piece at cl and fl file). The first move involves pushing the
pawn at g2 to g3. Once the pawn moves, the bishop can go to the 2nd
rank. Express these two moves (done by the player on the white side) in
vector form and find the angle between these two vectors. (Note that:
Bishop can develop diagonally)
Solution
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