Answer to Question #203439 in Analytic Geometry for Master j

Question

Represent the forces 𝐹₁ = 3𝑗 − 𝑖 and 𝐹₂ = 3𝑖 + 5𝑗, on graph paper, showing both forces acting on an object at the point (0, 0). Complete the diagram to show the magnitude and direction of the resultant force 𝐹𝑅.

Answer 1

Solution:

𝐹₁ = 3𝑗 − 𝑖 and 𝐹₂ = 3𝑖 + 5𝑗

𝐹₁ = − 𝑖 +3𝑗 and 𝐹₂ = 3𝑖 + 5𝑗

So, 𝐹₁=(-1,3) and 𝐹₂=(3,5).

Now, clear $F_R+F_1=F_2$

$F_R=F_2-F_1= 3 \hat𝑖 + 5\hat𝑗-(3\hat𝑗 − \hat𝑖 )=4\hat i-2\hat j$