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These are the component forms of vectors vec(e) and vec(f) : {:[ vec(e)=(3","5)],[ vec(f)=(1","-6)]:} Add the vectors. vec(e)+ vec(f)=(◻,◻)

These are the component forms of vectors e⃗ \vec{e} and f⃗ \vec{f} :\newlinee⃗=(3,5)f⃗=(1,−6) \begin{array}{l} \vec{e}=(3,5) \\ \vec{f}=(1,-6) \end{array} \newlineAdd the vectors.\newlinee⃗+f⃗=(□,□) \vec{e}+\vec{f}=(\square, \square)

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Full solution

Q. These are the component forms of vectors e⃗ \vec{e} and f⃗ \vec{f} :\newlinee⃗=(3,5)f⃗=(1,−6) \begin{array}{l} \vec{e}=(3,5) \\ \vec{f}=(1,-6) \end{array} \newlineAdd the vectors.\newlinee⃗+f⃗=(□,□) \vec{e}+\vec{f}=(\square, \square)
  1. Identify Components: Identify the components of each vector. e⃗\vec{e} has components (3,5)(3, 5). f⃗\vec{f} has components (1,−6)(1, -6). To add two vectors, we add their corresponding components.
  2. Add X-Components: Add the corresponding x-components of e⃗\vec{e} and f⃗\vec{f}. The x-component of e⃗+f⃗\vec{e} + \vec{f} is 3+1=43 + 1 = 4.
  3. Add Y-Components: Add the corresponding y-components of e⃗\vec{e} and f⃗\vec{f}. The y-component of e⃗+f⃗\vec{e} + \vec{f} is 5+(−6)=−15 + (-6) = -1.
  4. Combine Results: Combine the results from Step 22 and Step 33 to form the new vector. e⃗+f⃗=(4,−1)\vec{e} + \vec{f} = (4, -1).

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