Question

Vector u has initial point P at (0, 0) and terminal point Q at (5, -8). What are the component form and magnitude of u?
• u = (5, -8): ||u|| = -√89
• u = (5, 8): ||u|| = -√89
• u = (5, -8): ||u|| = √89
• u = (5, 8): ||u|| = √89

Answer 1

The correct option for the given vector is the third one:

• u = (5, -8): ||u|| = √89

What are the component form and magnitude of u?

If the initial point is (0, 0), then the component form of the vector is just equal to the terminal point of the vector.

Then we have:

u = (5, -8)

For a vector w = (x, y) the magnitude is:

$||w|| = \sqrt{x^2 + y^2}$

In this case, the magnitude will be:

$||u|| = \sqrt{5^2 + (-8)^2} = \sqrt{89}$

Then the correct option is the third one.

If you want to learn more about vectors:

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