Find the sum of two vectors if one has a direction of 65° and a magnitude of 10, and the other has a direction of 35° and a magnitude of 15.
A)magnitude of 25 at direction of 100°
B)magnitude of 5 at direction of 30°
C)magnitude of 24.2 at direction of 46.9°
D)magnitude of 24.2 at direction of 100°

Question

Quizplus · Accepted Answer

To find the sum of two vectors, we need to break each vector into its x and y components.

For the first vector with direction 65° and magnitude 10, we have:

x component: 10 cos 65° ≈ 3.42
y component: 10 sin 65° ≈ 8.66

For the second vector with direction 35° and magnitude 15, we have:

x component: 15 cos 35° ≈ 12.27
y component: 15 sin 35° ≈ 8.57

To find the sum of the two vectors, we add the x components and the y components separately:

x component: 3.42 + 12.27 ≈ 15.69
y component: 8.66 + 8.57 ≈ 17.23

Now we can use the Pythagorean theorem to find the magnitude of the sum vector:

magnitude = sqrt((15.69)^2 + (17.23)^2) ≈ 24.2

And we can use trigonometry to find the direction of the sum vector:

tan θ = y / x = 17.23 / 15.69
θ ≈ 46.9°

So the answer is C: magnitude of 24.2 at direction of 46.9°.

Find the Sum of Two Vectors If One Has a Direction