Question:
What is the length of the projection of \( 3\hat{i} + 4\hat{j} + 5\hat{k} \) on the xy-plane?
What is the length of the projection of \( 3\hat{i} + 4\hat{j} + 5\hat{k} \) on the xy-plane?
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The projection of a vector on the xy-plane removes the \( z \)-component, and the magnitude is calculated using the remaining components.
Updated On: Jan 12, 2026
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The Correct Option is B
Solution and Explanation
Step 1: The projection of a vector \( \mathbf{v} = 3\hat{i} + 4\hat{j} + 5\hat{k} \) on the xy-plane is given by the vector \( \mathbf{v}_{xy} = 3\hat{i} + 4\hat{j} \).
Step 2: The length of the projection is the magnitude of \( \mathbf{v}_{xy} \): \[ \left| \mathbf{v}_{xy} \right| = \sqrt{3^2 + 4^2} = 5. \]
Final Answer: \[ \boxed{5} \]
Step 2: The length of the projection is the magnitude of \( \mathbf{v}_{xy} \): \[ \left| \mathbf{v}_{xy} \right| = \sqrt{3^2 + 4^2} = 5. \]
Final Answer: \[ \boxed{5} \]
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