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

Dec 1, 2015

The magnitude of the resultant is $\approx \text{11 units}$.

#### 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 $a = 8.7 \mathmr{and} b = 6.5$

${c}^{2} = \left({8.7}^{2} + {6.5}^{2}\right)$

Take the square root of both sides.

$c = \sqrt{{8.7}^{2} + {6.5}^{2}}$

$c = 10.8 \approx \text{11 units}$ (rounded to two significant figures)

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