# a. Are the vectors in equilibrium? b. If not, find the magnitude and the direction of the resultant force.Three forces in a plane act on an object. The forces are 7 N, 11 N, and 15 N. The angle...

a. Are the vectors in equilibrium?

b. If not, find the magnitude and the direction of the resultant force.

Three forces in a plane act on an object. The forces are 7 N, 11 N, and 15 N. The angle between the 7 N and 11 N forces is 105°, between the 11 N and 15 N forces is 147°, and between the 15 N and 7 N forces is 108°.

I've been having a hard time trying to set up and solve for this problem.

Applications with Vectors

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### 1 Answer

Let force 7N is at the direction of positive Y-axis.

Let force 11N is at the right side of 7N and force 15 is at left side.

Let unit vector to X-axis is i and unit vector to Y-axis is j

The;

force 7N = 0*i+7*j

force 11N = 11cos 15*i-11sin15*j = 10.625*i-2.847*j

force 15N = -15cos18*i-15sin18*j = -14.266*i-4.635*j

Vector addition[force 7N+force 11N+force 15N]

=0*i+7*j+10.625*i-2.847*j-14.266*i-4.635*j

= -3.641*i-0.482*j

a) since vector addition of forces are not zero the forces are not at equilibrium.

b) The resultant force (R) = sqrt[(-3.641)^2+(-0.482)^2]

= 3.672N

The direction of resultant force = tan^(-1)(-0.482/-3.641)

= 7.54 deg.

**The resultant is 3.672N at an anticlockwise angle of 7.54 deg. to the X-axis.**

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