Two vectors, A and B are defined in the picture above. Each of the small squares

Question

Two vectors, A and B are defined in the picture above. Each of the small squares on the picture measures 1.00 m by 1.00 m. Both of the vectors start at the origin, and end at an intersection point of the grid lines.

By using the vector sum of integer multiples of these two vectors (for instance, 5 times the vector A added to ?9 times vector B), you can reach quite a number of grid points (including many grid points off the picture), starting from the origin. Let's say you want to reach the grid point at

x = 70 m and y = -26 m .

What integers would you multiply A and B by? Again, you're reaching the specified grid point by adding, as vectors, some integer times A plus some integer times B.

To get to the specified point, you do:

_______A + ________B

Explanation / Answer

A = -1i + 2j B = 3i for R = 70I -26j here j component only by A so -13 x A = -26j + 13i 19 x B = 57i R = -13 A + 19B

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