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Given vectors u = (1, 2) and v = (6,2), find the difference v – u and represent

the difference graphically in two different ways.

1 Answer

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Final answer:

To find the difference between vectors v and u, subtract the corresponding components. The graphical representation of the difference can be done by plotting the vectors and drawing the resulting vector from the initial point of v to the initial point of u. Alternatively, the difference can be represented as a displacement vector.

Step-by-step explanation:

The difference between vectors v and u is found by subtracting the corresponding components of each vector. So, v - u = (6 - 1, 2 - 2) = (5, 0).

To represent the difference graphically, we can plot the vectors v and u on a coordinate plane and draw the resulting vector from the initial point of v to the initial point of u. This would give us a vector pointing in the opposite direction of the original vector u, with the magnitude equal to the difference between the x-components of v and u.

Alternatively, we can also represent the difference v - u as a displacement vector. If we imagine taking steps forward according to the components of vector v, and then subtracting the steps forward according to the components of vector u, we would be left with the difference vector (5, 0), which represents the remaining steps forward.

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