Question

Three vectors are given in standard position.

-->
A=190 at 0A=218 deg
-->
B=241 at 0B=115 deg
-->
c=137 at 0c=334 deg
Find the magnitude (resultant). Round answer to the nearest
whole number.

Answer 1

To find the magnitude of a resultant vector, resolve each vector into its x and y components, sum these components, and then use the Pythagorean theorem to calculate the magnitude of the resultant.

Step-by-step explanation:

To find the magnitude of the resultant of three vectors A, B, and C given in standard position, we must first resolve each vector into its horizontal (x) and vertical (y) components.

For each vector, the x-component is found by multiplying the magnitude of the vector by the cosine of its direction angle, and the y-component is found by multiplying the magnitude of the vector by the sine of its direction angle.

Once the components are found, they are summed for all the vectors to find the resultant's x and y components. The magnitude of the resultant vector R is then found using the Pythagorean theorem:

R = √(Rx² + Ry²)

Let's apply these steps to the given vectors:

Resolve each vector into its x and y components:

Vector A: Ax = 190 cos(218°), Ay = 190 sin(218°)

Vector B: Bx = 241 cos(115°), By = 241 sin(115°)

Vector C: Cx = 137 cos(334°), Cy = 137 sin(334°)

Sum the x and y components separately to find Rx and Ry.

Calculate the magnitude R using the Pythagorean theorem.

Finally, you round the resultant to the nearest whole number as instruction