Find the magnitude and direction of r + u

Option a: magnitude = 1.6 cm and angle = 40.3°

Step-by-step explanation:

This problem consists of a sum of vectors

To make this sum, we need to decompose each vector in x and y components, using their angles.

So, for vector u, we have:

u_x = u*cos(340) = 3 * 0.9397 = 2.8191

u_y = u*sin(340) = 3 * (-0.342) = -1.026

Now for vector r we have:

r_x = r*cos(128) = 2.6 * (-0.6157) = -1.6008

r_y = r*sin(128) = 2.6 * 0.788 = 2.0488

Now we need to sum the x components and the y components to find the resultant of r + u. Let's call the resultant vector k:

k_x = u_x + r_x = 2.8191 - 1.6008 = 1.2183

k_y = u_y + r_y = -1.026 + 2.0488 = 1.0228

To find the magnitude and the angle, we can use Pythagoras's formula and arc tangent of k_y/k_x:

magnitude = sqrt(1.2183^2 + 1.0228^2) = 1.5907 cm

angle = arc tangent(1.0228/1.2183) = 40.0145°

So the nearest answer is option a: magnitude = 1.6 cm and angle = 40.3°

the one where 1 and 2 are directly across from each other.  

see image