Question

If the projection of $\overrightarrow{PQ}$ on OX, OY, OZ are respectively 12, 3 and 4, then the magnitude of $\overrightarrow{PQ}$ is

• A. $169$
• B. $19$
• C. $13$
• D. $144$

Hint:

The projections on axes are the components of the vector.

Answer 1

The Correct Option is C

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 $13$.