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Find the specified vector or scalar. Show your work.

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

User RCalaf
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1 Answer

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We sum vectors by summing the coefficient of corresponding coordinates:


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

So, in your case, we have


u+v = (-4+4)i + (1+1)j = 0i+2j = 2j

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


u = ai+bj \implies ||u||=√(a^2+b^2)

So, in your case, we have


||u+v|| = ||0i+2j|| = √(0^2+2^2) = √(4)=2

User ArrayOutOfBound
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