Question

if the x and y vector components of vector a are 11 and 7, what is the magnitude of vector a? round your answer to the nearest hundredth.

Explanation:

Step1: Recall magnitude formula

The magnitude of a 2 - D vector $\vec{A}$ with $x$-component $A_x$ and $y$-component $A_y$ is given by $|\vec{A}|=\sqrt{A_x^{2}+A_y^{2}}$. Here $A_x = 11$ and $A_y=7$.

Step2: Substitute values

$|\vec{A}|=\sqrt{11^{2}+7^{2}}=\sqrt{121 + 49}=\sqrt{170}$.

Step3: Calculate the square - root

$\sqrt{170}\approx13.04$.

Answer:

$13.04$