# What is the resultant vector for the following?Two vectors F1 and F2 where F1 = 34 N and F2= 65 N with F1 forming an angle of 240 degrees and F2 an angle of 25 degrees with the positive x-axis and...

What is the resultant vector for the following?

Two vectors F1 and F2 where F1 = 34 N and F2= 65 N with F1 forming an angle of 240 degrees and F2 an angle of 25 degrees with the positive x-axis and a counter-clockwise rotation being considered positive.

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### 1 Answer

The two vectors provided are F1 and F2 which have a magnitude of 34 N and 65 N resp. and which form an angle of 240 degrees and 25 degrees resp. with the positive x- axis.

Now we split the two vectors into their x and y components.

We see that F1x = -34* sin 30 and F1y = -34 * cos 30.

For the vector F2, F2x = 65 *cos 25 and F2y = 65*sin 25.

Let the resultant vector be denoted as F.

Fx = 65*cos 25 - 34*sin 30 = 41.91

Fy = 65*sin 25 - 34*cos 30 = -1.97

The magnitude of the resultant vector is sqrt (41.91^2 + 1.97^2)

=> 41.95 N

The direction of the resultant vector is arc tan ( 41.91/(-1.97)) = -87.3 degrees.

Therefore the required resultant vector of the given vectors has a magnitude of 41.95 N and an angle of -87.3 degrees to the positive x-axis.