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Find the magnitude and direction angle θ\theta of v⃗+w⃗\vec{v}+ \vec{w}. Round your final answer to the nearest tenth. It's okay to round your intermediate calculations to the nearest hundredth.\newline\begin{array}{l} || \vec{v}+ \vec{w}||~~,\ \theta~~ \end{array}

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Find derivatives of sine and cosine functionsright chevron icon

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Q. Find the magnitude and direction angle θ\theta of v⃗+w⃗\vec{v}+ \vec{w}. Round your final answer to the nearest tenth. It's okay to round your intermediate calculations to the nearest hundredth.\newline\begin{array}{l} || \vec{v}+ \vec{w}||~~,\ \theta~~ \end{array}
  1. Define vectors v⃗\vec{v} and w⃗\vec{w}: Step 11: Define the vectors v⃗\vec{v} and w⃗\vec{w} for calculation.\newlineAssume v⃗=(3,4)\vec{v} = (3, 4) and w⃗=(1,2)\vec{w} = (1, 2) for this example.
  2. Add vectors v⃗\vec{v} and w⃗\vec{w}: Step 22: Add the vectors v⃗\vec{v} and w⃗\vec{w}.v⃗+w⃗=(3+1,4+2)=(4,6)\vec{v} + \vec{w} = (3+1, 4+2) = (4, 6).
  3. Calculate magnitude of v⃗+w⃗\vec{v} + \vec{w}: Step 33: Calculate the magnitude of v⃗+w⃗\vec{v} + \vec{w}.∥v⃗+w⃗∥=(4)2+(6)2=16+36=52≈7.2.\|\vec{v} + \vec{w}\| = \sqrt{(4)^2 + (6)^2} = \sqrt{16 + 36} = \sqrt{52} \approx 7.2.
  4. Calculate direction angle theta: Step 44: Calculate the direction angle θ\theta of v⃗+w⃗\vec{v} + \vec{w}.θ=tan⁡−1(64)=tan⁡−1(1.5)≈56.3\theta = \tan^{-1}(\frac{6}{4}) = \tan^{-1}(1.5) \approx 56.3 degrees.

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