Question

5. given the vector [-5,12], find each of the following vectors. a. same direction, twice as long. b. same direction, length 1 (unit vector) c. opposite direction, length 10 d. opposite direction, length c.

Answer 1

The vectors are listed below:

1. v = [- 10 / 13, 24 / 13]
2. v = [- 5 / 13, 12 / 13]
3. v = [50 / 13, - 120 / 13]

How to derive the expressions of vectors

Vectors are characterized by magnitude and direction. The magnitude is a scalar and the direction by a ordered pair, whose formula is shown below:

v = k · u    

Where u is a unit vector, that is, a vector of length 1.

Now we proceed to determine each vector:

a) The equation of the vector:

r = √[(- 5)² + 12²]

r = 13

k = 2

v = (2 / 13) · [- 5, 12]

v = [- 10 / 13, 24 / 13]

b) The equation of the vector:

v = (1 / 13) · [- 5, 12]

v = [- 5 / 13, 12 / 13]

c) The equation of the vector:

v = (- 10 / 13) · [- 5, 12]

v = [50 / 13, - 120 / 13]

To learn more on vectors: brainly.com/question/4579006

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