Question

vector e is 102 units up and vector f is 94 units right. vector r is equal to vector e + vector f.

Explanation:

Step1: Identify vector components

Vector E has y - component \(E_y = 102\) and x - component \(E_x=0\). Vector F has x - component \(F_x = 94\) and y - component \(F_y = 0\).

Step2: Calculate components of vector R

For the x - component of R, \(R_x=E_x + F_x=0 + 94=94\). For the y - component of R, \(R_y=E_y+F_y = 102+0 = 102\).

Step3: Find the magnitude of vector R

Using the Pythagorean theorem \(|R|=\sqrt{R_x^{2}+R_y^{2}}=\sqrt{94^{2}+102^{2}}=\sqrt{8836 + 10404}=\sqrt{19240}\approx138.71\).

Step4: Find the direction of vector R

The direction \(\theta=\arctan(\frac{R_y}{R_x})=\arctan(\frac{102}{94})\approx47.3^{\circ}\) above the positive x - axis.

Answer:

Vector R has a magnitude of approximately 138.71 units and is directed at an angle of approximately \(47.3^{\circ}\) above the positive x - axis.