Brainilt
Brainilt Brainilt
  • 12-05-2019
  • Mathematics
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Find the specified vector or scalar. Show your work.

u = -4i + 1j and v = 4i + 1j; Find ‖u+v‖

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Аноним Аноним
  • 12-05-2019

We sum vectors by summing the coefficient of corresponding coordinates:

[tex]v = ai+bj,\quad w = ci+dj \implies v+w = (a+c)i+(b+d)j[/tex]

So, in your case, we have

[tex]u+v = (-4+4)i + (1+1)j = 0i+2j = 2j[/tex]

The norm of a vector is the square root of the sum of the squares of its coefficients:

[tex]u = ai+bj \implies ||u||=\sqrt{a^2+b^2}[/tex]

So, in your case, we have

[tex]||u+v|| = ||0i+2j|| = \sqrt{0^2+2^2} = \sqrt{4}=2[/tex]

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