What is the resultant vector if a vector 7 units from the origin along the X axis is added to a vector 3 units along the Y axis?
Question
What is the resultant vector if a vector 7 units from the origin along the X axis is added to a vector 3 units along the Y axis?
Solution
To find the resultant vector of two vectors, we can use the Pythagorean theorem. Here are the steps:
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Identify the vectors: We have a vector of 7 units along the X-axis and a vector of 3 units along the Y-axis.
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Square each vector's magnitude: The square of the X vector's magnitude is 7^2 = 49, and the square of the Y vector's magnitude is 3^2 = 9.
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Add the squares: The sum of the squares is 49 + 9 = 58.
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Take the square root of the sum: The square root of 58 is approximately 7.62.
So, the resultant vector when a vector of 7 units along the X-axis is added to a vector of 3 units along the Y-axis is approximately 7.62 units.
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