If Vector u=(5,-7) and v=(-11,3), 2v-6u=_ and ||2v-6u||≈_

[tex]2\vec{v}-6\vec{u} \\ \\ Replace \ \vec{v} \ and \ \vec{u} \ by \ the \ given \ vectors: \\ \\ 2(-11,3)-6(5,-7) \\ \\ Multiply \ each \ component \ by \ the \ corresponding \ scalar:\\ \\ (2\times (-11),2\times 3)+(-6\times 5,-6\times (-7)) \\ \\ (-22,6)+(-30,42) \\ \\ Sum \ of \ vectors: \\ \\ (-22-30,6+42) \\ \\ \therefore \boxed{(-52,48)}[/tex]

SECOND:

If we name:

[tex]\vec{w}=2\vec{v}-6\vec{u}[/tex]

Then, [tex]||2\vec{v}-6\vec{u}||[/tex] is the magnitude of the vector [tex]\vec{w}[/tex]. Therefore:

[tex]||\vec{w}||=||2\vec{v}-6\vec{u}|| \\ \\ ||\vec{w}||=||(-52,48)|| \\ \\ ||\vec{w}||=\sqrt{(-58)^2+48^2} \\ \\ ||\vec{w}||=\sqrt{3364+2304} \\ \\ ||\vec{w}||=\sqrt{5668} \\ \\ \boxed{||\vec{w}||=75.28}[/tex]

pinquancaro pinquancaro · Answer 2 · 2019-06-25T11:33:27+02:00

Answer:

[tex]2v-6u=(-52,48)[/tex]

[tex]||2\vec{v}-6\vec{u}||=75.28[/tex]

Step-by-step explanation:

Given : If Vector u=(5,-7) and v=(-11,3)

To find : The value of 2v-6u and ||2v-6u||?

Solution :

We have given,

[tex]\vec{u}=(5,-7)[/tex] and [tex]\vec{v}=(-11,3)[/tex]

Substitute in [tex]2v-6u[/tex]

[tex]= 2(-11,3)-6(5,-7)[/tex]

[tex]= (2\times (-11),2\times 3)+(-6\times 5,-6\times (-7))[/tex]

[tex]=(-22,6)+(-30,42)[/tex]

Adding the two vectors,

[tex]=(-22-30,6+42)[/tex]

[tex]=(-52,48)[/tex]

So, [tex]2v-6u=(-52,48)[/tex]

Now, we find the value of [tex]||2\vec{v}-6\vec{u}||[/tex]

Substitute the value,

[tex]||2\vec{v}-6\vec{u}||=||(-52,48)|| \\ \\ ||||2\vec{v}-6\vec{u}||=\sqrt{(-58)^2+48^2} \\ \\ ||||2\vec{v}-6\vec{u}||=\sqrt{3364+2304} \\ \\ ||2\vec{v}-6\vec{u}||=\sqrt{5668} \\ \\||2\vec{v}-6\vec{u}||=75.28[/tex]

So, [tex]||2\vec{v}-6\vec{u}||=75.28[/tex]

If Vector u=(5,-7) and v=(-11,3), 2v-6u=_____ and ||2v-6u||≈_____

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Answer:

Step-by-step explanation:

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If Vector u=(5,-7) and v=(-11,3), 2v-6u=_ and ||2v-6u||≈_