Question:
If the projection of $\overrightarrow{PQ}$ on OX, OY, OZ are respectively 12, 3 and 4, then the magnitude of $\overrightarrow{PQ}$ is
If the projection of $\overrightarrow{PQ}$ on OX, OY, OZ are respectively 12, 3 and 4, then the magnitude of $\overrightarrow{PQ}$ is
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The projections on axes are the components of the vector.
Updated On: May 2, 2026
- $169$
- $19$
- $13$
- $144$
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
Projections on coordinate axes are the components of the vector.
Step 2: Detailed Explanation:
If $l, m, n$ are the projections (direction cosines times magnitude), then the vector $\overrightarrow{PQ} = 12\hat{i} + 3\hat{j} + 4\hat{k}$.
Magnitude $|\overrightarrow{PQ}| = \sqrt{12^2 + 3^2 + 4^2} = \sqrt{144 + 9 + 16} = \sqrt{169} = 13$.
Step 3: Final Answer:
The magnitude is $13$.
Projections on coordinate axes are the components of the vector.
Step 2: Detailed Explanation:
If $l, m, n$ are the projections (direction cosines times magnitude), then the vector $\overrightarrow{PQ} = 12\hat{i} + 3\hat{j} + 4\hat{k}$.
Magnitude $|\overrightarrow{PQ}| = \sqrt{12^2 + 3^2 + 4^2} = \sqrt{144 + 9 + 16} = \sqrt{169} = 13$.
Step 3: Final Answer:
The magnitude is $13$.
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