The force on an object is F⃗ =−17j⃗ . For the vector v⃗ =2i⃗ +3j⃗ , find: (a) The component of F⃗ parallel to v⃗

(a) , (b) , (c)

Explanation:

The statement is incomplete:

The force on an object is . For the vector . Find: (a) The component of parallel to , (b) The component of perpendicular to , and (c) The work , done by force through displacement .

(a) The component of parallel to is determined by the following expression:

Where is the unit vector of , which is determined by the following expression:

Where is the norm of , whose value can be found by Pythagorean Theorem.

Then, if and , then:

(b) Parallel and perpendicular components are orthogonal to each other and the perpendicular component can be found by using the following vectorial subtraction:

Given that and , the component of perpendicular to is:

(c) The work done by   through displacement is: