Question

The `x` component of a vector is 8.7 units, and its `y` component is 06.5 units. What is the magnitude?

Answer 1

The magnitude of the resultant is `~~"11 units"`.

Explanation:

Since one vector is on the x-axis and the other is on the y-axis, we can use a right triangle and the Pythagorean theorem to determine the magnitude of the resultant, which is the hypotenuse.

Pythagorean Theorem

`c^2=a^2+b^2`, where `a=8.7 and b=6.5`

`c^2=(8.7^2+6.5^2)`

Take the square root of both sides.

`c=sqrt(8.7^2+6.5^2)`

`c=10.8~~"11 units"` (rounded to two significant figures)

Note: The values for `a` and `b` could have been reversed with the same result.