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The x and y components of a position vector P have numerical values 5 and 6 respectively . direction and magnitude of the vectorP?
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The x and y components of a position vector P have numerical values 5 ...
Understanding the Position Vector P
The position vector P is defined by its components along the x and y axes. In this case, the x-component is 5 and the y-component is 6.

Magnitude of Vector P
The magnitude of a vector can be calculated using the formula:
\[ |P| = \sqrt{x^2 + y^2} \]
For our vector P:
- x = 5
- y = 6
Calculating the magnitude:
- |P| = \(\sqrt{5^2 + 6^2}\)
- |P| = \(\sqrt{25 + 36}\)
- |P| = \(\sqrt{61}\)
- |P| ≈ 7.81

Direction of Vector P
The direction of a vector is determined by its angle θ with respect to the positive x-axis. This can be found using the tangent function:
\[ \tan(θ) = \frac{y}{x} \]
For our vector P:
- y = 6
- x = 5
Calculating the angle:
- \(\tan(θ) = \frac{6}{5}\)
- θ = \(\arctan\left(\frac{6}{5}\right)\)
- θ ≈ 50.19 degrees

Summary
- **Magnitude of Vector P:** ≈ 7.81
- **Direction of Vector P:** ≈ 50.19 degrees from the positive x-axis
Understanding both the magnitude and direction equips one to analyze and apply the position vector effectively in physics and mathematics.
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The x and y components of a position vector P have numerical values 5 and 6 respectively . direction and magnitude of the vectorP?
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