Ask a question

Applications of the Dot Product (Vectors)

A force, F of 25 N is acting in the direction of a = (6,1). 
a) Find a unit vector in the direction of a.
b) Find the Cartesian vector representing the force, f, using your answer from part a)

1 Answer by Expert Tutors

Tutors, sign in to answer this question.
Francisco E. | Francisco; Civil Engineering, Math., Science, Spanish, Computers.Francisco; Civil Engineering, Math., Sci...
5.0 5.0 (1 lesson ratings) (1)
The unit vector will be: F/¦F¦(magnitude); I suppose that the vector tail is located at the origin. Then the angle that the line oa  (direction) makes over x axis (φ) will be tan-1 (1/6) = 9.46 degrees, then cosine φ = 0.9864 and sin φ is= 0.1644. the vector components of the 25N vector are V= 24.66i + 4.11j and the magnitude of the vector will be √((Vx^2)+(Vy^2)) = √625= 25 Ok!!!!!!!!!!. The unit vector will be a= (24.66/25)i + (4.11/25)j= 0.9864i + 0.1644j
The Cartesian vector will be a*25 = 24.66i + 4.11j