Respuesta :

v=|v|(i cosθ + j sinθ)
=14(i cos225 + j sin225)
=14(-[tex] \frac{ \sqrt{2} }{2} [/tex] i + -[tex] \frac{ \sqrt{2} }{2} [/tex] j)
=(-7[tex] \sqrt{2} [/tex] i + -7[tex] \sqrt{2} [/tex] j)

The vector v in terms of [tex]i[/tex] and [tex]j[/tex] is [tex]-9.8i-9.8j[/tex].

Vector components  from magnitude and direction

The components of a vector with magnitude ||v|| and direction θ are

( ||v||cosθ, ||v||sinθ ).

According to the given question we have  

magnitude, ||v|| = 14

θ = 225 degrees

Therefore,

[tex]v_{x}[/tex] = ||v||cosθ = 14cos225 = 14×(-0.70) = -9.8

[tex]v_{y}[/tex] = ||v||sinθ = 14sin225 =  14×(-0.701) = -9.8

since,

[tex]v=v_{x}i +v_{y}j[/tex]

substitute the value of  [tex]v_{x}[/tex]  and [tex]v_{y}[/tex] in the above expression

⇒ [tex]v=-9.8i-9.8j[/tex]

Hence, the vector v in terms of [tex]i[/tex] and [tex]j[/tex] is [tex]-9.8i-9.8j[/tex].

Learn more about vector component here:

https://brainly.com/question/22056199

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