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A vector is represented by 4i+2j+2k. It ...

A vector is represented by `4i+2j+2k`. It is length in the XOY plane is

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To find the length of the vector `4i + 2j + 2k` in the XOY plane, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the components of the vector**: The vector is given as `4i + 2j + 2k`. Here, the components are: - x-component (i): 4 - y-component (j): 2 - z-component (k): 2 2. **Consider only the X and Y components**: Since we are interested in the length of the vector in the XOY plane, we will only consider the i and j components. The k component (which is along the z-axis) is not relevant for this calculation. 3. **Use the formula for the length of a vector in the XOY plane**: The length (or magnitude) of a vector in the XOY plane can be calculated using the formula: \[ \text{Length} = \sqrt{(x^2 + y^2)} \] Here, \( x = 4 \) and \( y = 2 \). 4. **Substitute the values into the formula**: \[ \text{Length} = \sqrt{(4^2 + 2^2)} = \sqrt{(16 + 4)} = \sqrt{20} \] 5. **Simplify the expression**: \[ \sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5} \] 6. **Final Answer**: The length of the vector `4i + 2j + 2k` in the XOY plane is \( 2\sqrt{5} \) units.
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