Answer:
(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:
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