(a) A video camera is supported by three wires.

Tension and directed angle of each wire is given.

Use Tension and directed angle of each wire to write the component form of the vectors representing each of the wires.

Component form of a vector is .

For wire 1, the directed angle is and the tension is 1200 N.

Component form of a vector of wire 1 is

For wire 2, the directed angle is and the tension is 1000 N.

Component form of a vector of wire 2 is

.

For wire 3, the directed angle is and the tension is 700 N.

Component form of a vector of wire 3 is

.

(b) Component form of resultant vector acting on that camera is sum of the wire 1 vector , wire 2 vector and

wire 3 vector .

.

Substitute , and in above expression.

Component form of resultant vector is .

(c) Component form of resultant force vector is .

Find the magnitude of .

.

Magnitude of resultant force vector is 1157 N.

Find the directed angle of .

Directed angle of is

Thus,

.

The resultant force is about 1157 N and directed angle is .

(a) Component form of a vector of wire 1 is .

Component form of a vector of wire 2 is .

Component form of a vector of wire 3 is .

(b) Component form of resultant vector is .

(c) The resultant force is about 1157 N and directed angle is .