Question

Let vector u = [3, 2]

a) Determine each vector

i)
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]

Answer 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