[tex]v_1 = 7[/tex]
x = 4
y = 3
From the diagram, it is clear that the x and y are the component of the [tex]v_2[/tex] vector. Since, x and y are perpendicular.
Hence,
[tex]v_2 = \sqrt{x^2 + y^2}[/tex]
[tex]v_2 = \sqrt{4^2 + 3^2}[/tex]
[tex]v_2 =\sqrt{16 + 9}[/tex]
[tex]v_2 = \sqrt{25}\\[/tex]
[tex]v_2 = 5[/tex]
Now, [tex]v_1[/tex] and x are in the same direction. Hence, we can add the magnitude.
[tex]= v_1 + x[/tex]
= 7 + 4
[tex]v_1 + x= 11[/tex]
y and [tex](v_1 + x)[/tex] are perpendicular and they are the components of R
Hence, the magnitude of R:
[tex]R = \sqrt{(v_1 +x)^2 + y^2}[/tex]
[tex]R = \sqrt{11^2 + 3^2} =\sqrt{121 +9} = \sqrt{130}[/tex]
R = 11.4
