Find the quantity if v = 5i - 7j and w = 3i + 2j.
-$\| v \| - \| w \|$
A) $\sqrt { 85 }$
B) $2 \sqrt { 6 } - \sqrt { 13 }$
C) $\sqrt { 74 } - \sqrt { 13 }$
D) $\sqrt { 11 }$

Question

Quizplus · Accepted Answer

The magnitude of vector $v = 5i - 7j$ is $\| v \| = \sqrt{5^2 + (-7)^2} = \sqrt{25 + 49} = \sqrt{74}$. The magnitude of vector $w = 3i + 2j$ is $\| w \| = \sqrt{3^2 + 2^2} = \sqrt{9 + 4} = \sqrt{13}$. Therefore, $\| v \| - \| w \| = \sqrt{74} - \sqrt{13}$.

Find the Quantity If V = 5i - 7j and W