QuestionJuly 15, 2025

Find the degree to th nearest tenth and direction of the vector. [} 10 24 ]

Find the degree to th nearest tenth and direction of the vector. [} 10 24 ]
Find the degree to th nearest tenth and direction of the vector. [} 10 24 ]

Solution
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Answer

67.4^\circ, direction is above the positive x-axis. Explanation 1. Calculate the magnitude Use the formula for magnitude: \sqrt{x^2 + y^2}. Here, x = 10 and y = 24. So, magnitude = \sqrt{10^2 + 24^2} = \sqrt{100 + 576} = \sqrt{676} = 26. 2. Calculate the angle in degrees Use the formula \theta = \tan^{-1}\left(\frac{y}{x}\right). Here, \theta = \tan^{-1}\left(\frac{24}{10}\right). 3. Convert radians to degrees Calculate \theta using a calculator: \theta \approx \tan^{-1}(2.4) \approx 67.38^\circ. 4. Round to nearest tenth Round 67.38^\circ to 67.4^\circ.

Explanation

1. Calculate the magnitude<br /> Use the formula for magnitude: $\sqrt{x^2 + y^2}$. Here, $x = 10$ and $y = 24$. So, magnitude = $\sqrt{10^2 + 24^2} = \sqrt{100 + 576} = \sqrt{676} = 26$.<br />2. Calculate the angle in degrees<br /> Use the formula $\theta = \tan^{-1}\left(\frac{y}{x}\right)$. Here, $\theta = \tan^{-1}\left(\frac{24}{10}\right)$.<br />3. Convert radians to degrees<br /> Calculate $\theta$ using a calculator: $\theta \approx \tan^{-1}(2.4) \approx 67.38^\circ$.<br />4. Round to nearest tenth<br /> Round $67.38^\circ$ to $67.4^\circ$.
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