Find the sum of the following two vectors: (i)50 units due east and (ii)100 units 30° south of west.
A)100 units 30° south of west
B)62 units 54° south of west
C)87 units 60° south of west
D)62 units 15° south of west

Question

Quizplus · Accepted Answer

To find the sum of the two vectors, we first break them into their components. The first vector is 50 units due east, so its components are (50, 0). The second vector is 100 units 30° south of west, which means its components can be found using trigonometry: its x-component (westward) is $100 \cos(30^\circ)$ and its y-component (southward) is $100 \sin(30^\circ)$. Thus, its components are $(-100 \cos(30^\circ), -100 \sin(30^\circ))$ or approximately $(-86.6, -50)$. Adding the components of the two vectors gives us $(50 - 86.6, 0 - 50) = (-36.6, -50)$. The magnitude of the resultant vector is $\sqrt{(-36.6)^2 + (-50)^2} \approx 62$ units, and the direction can be found using the tangent function: $\tan^{-1}\left(\frac{-50}{-36.6}\right) \approx 54^\circ$ south of west.

Find the Sum of the Following Two Vectors: (I)50 Units