Add the following vectors A 326 A 174 and B 275 B 338 No

Add the following vectors: A = 326, A = 174° and B = 275, B = 338° (Note: if PIN = 32756, then 326 = 349) Round your answers to one decimal place. **the last answer wasn\'t very clear on the step process took to come up with answer A+B = ( - 350+255.9 , 36.8 - 103.3) A+B = ( - 94.2 , - 66.6)

Solution

You can find the x and y components of each vector, then add x\'s, then add y\'s. The vector sum can then be found


Note that 174 degrees is in the 2^nd quadrant where sin is +ve and cos -ve 174 – 90 = 84 is the angle the vector makes with

the x-axis


Vector B is in the 4th quadrant where the cos is positive and sin is negative 360 – 338 = 22 is the angle B makes with the x-axis

Ax + Bx = -A*cos4 + B*cos12

Ax + Bx = -326*0.9976 + 275*0.9781

Ax + Bx = -56.24

Ay + By = A*sin4 – B*sin12 = 326*0.0698 – 275*0.2079 = -34.42

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These magnitudes both being negative means the resultant vector is in the 3rd quadrant Call the resultant vector C

C = 65.94
This is the magnitude of the resultant vector, C
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The angle, a with the x-axis is:

Cos(a) = 56.24/34.42 = 52.26
This angle is in the 3rd quadrant, so I have to add 180 degrees
a + 180 = 232.26
So, the answer is: 65.94 angle 232.26