Question

Find the magnitude of u using the dot product. Write the result in radical form or decimal form, rounded to the nearest hundredth.

Answer 1

The vector is given as,

$u\text{ = }\langle\text{ -5, -6 }\rangle$

The magnitude of the vector u is given as,

$\parallel\text{ u }\parallel\text{ = }\sqrt{\text{ }\langle\text{ -5, -6 }\rangle\text{ . }\langle-5,\text{ -6 }\rangle}$

Calculating the dot product,

$\begin{gathered} \parallel\text{ u }\parallel\text{ = }\sqrt{(-5)(-6)+(-5)(-6)} \\ \parallel\text{ u }\parallel\text{ = }\sqrt{30\text{ + 30}} \\ \parallel\text{ u }\parallel\text{ =}\sqrt{60} \\ \parallel\text{ u }\parallel\text{ = 7.75} \end{gathered}$

Thus the required answer is,

$\begin{gathered} Radical\text{ form = }\sqrt{60} \\ Decimal\text{ form = 7.75} \end{gathered}$