Math - Algebraic Vectors

Let vector u = [3, 2]

a) Determine each vector

2u = 2[3, 2]
2u = [6, 4]

c) Determine the length of each vector in a.

MY QUESTION***** -------- Do you subtract the values to determine the length?

Length = 2u - u
Length = [6, 4] - [3, 2]
Length = [3, 4]

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  1. Do not confuse the problem of finding the length of a line segment if you know the two end points
    with finding the length of a vector.

    Suppose we have 2 points A(8,3) and B(11,7)

    then vector AB = [3,4]

    and │AB│ = √(3^2+4^2)
    = 5

    line segment AB = √((11-8)^2 + (7-3)^2)
    = 5

    when you write vector [a,b], and vectors can be drawn anywhere as long as they have the same direction and magnitude, one can assume the vector [a,b] to start at the origin (0,0) and end at the point(a,b).
    Hence we can say │[a,b]│ = √(a^2+b^2)

    in other words │[3,2]│ = √(9+4) = √13

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