Any questions? Asking and answering questions are equally educational for you.

Any questions? Asking and answering questions are equally educational for you.

Any questions? Asking and answering questions are equally educational for you.

Any questions? Asking and answering questions are equally educational for you.

Here you have known magnitudes and directions for two forces: F₁ and F₂. You are asked to find the magnitude and direction of the third force P such that the resultant of these three forces is zero.

Keep in mind that a vector equation in a plane has two independent sets of components. These two component equations are what you need to solve for the unknown magnitude and direction of P.

Any questions? Asking and answering questions are equally educational for you.

Recall that the unit vector directed from point a to point b is the position vector from a to b divided by the distance between a and b.

The three direction angles of a vector are the angles between the x-, y- and z-axes to the vector at the vector's base.  Recall from lecture how these directions are found from a unit vector.

Any questions? If so, ask here.

Recall that the unit vector directed from point a to point b is the position vector from a to b divided by the distance between a and b.

The three direction angles of a vector are the angles between the x-, y- and z-axes to the vector at the vector's base.  Recall from lecture how these directions are found from a unit vector.

Any questions? If so, ask here.

Recall from lecture how projections can be found using dot products. For Part a), you need to find F_AB as a vector, along with the unit vector that points along the cable AD, u_AD. The projection of F_AB onto the direction of AB is found using the dot product of  with the unit vector u_AD.

The dot product operation can also be used to find the cosine of the angle between two vectors.

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Again, recall the relationships between dot products and projections, as well as how the dot product of two vectors can be used to find the angle between those two vectors.

Any questions? If so, ask here.