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

Question

The lines $ \frac{1 - x}{2} = \frac{y - 1}{3} = \frac{z}{1} $ and $ \frac{2x - 3}{2p} = \frac{y}{-1} = \frac{z - 4}{7} $ are perpendicular to each other for $ p $ equal to:

Answer 1

Step 1: Basic Principle
Projections on coordinate axes are the components of the vector.
Step 2: Solution Procedure:
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: Required Answer:
The magnitude is $13$.

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 Correct Option is C

Solution and Explanation

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