Question:
\(\left\lVert 3\vec i-4\vec j-5\vec k\right\rVert =\) ?
\(\left\lVert 3\vec i-4\vec j-5\vec k\right\rVert =\) ?
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Magnitude \(=\sqrt{(\text{x-part})^2+(\text{y-part})^2+(\text{z-part})^2}\).
Updated On: Oct 17, 2025
- \(5\sqrt{2}\)
- \(12\)
- \(2\)
- \(9\)
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The Correct Option is A
Solution and Explanation
Idea. The length of a vector \(\langle a,b,c\rangle\) is the 3-D version of Pythagoras: \(\sqrt{a^2+b^2+c^2}\). Signs do not matter because we square.
Step. \[ \sqrt{3^2+(-4)^2+(-5)^2}=\sqrt{9+16+25}=\sqrt{50}=5\sqrt{2}. \]
Step. \[ \sqrt{3^2+(-4)^2+(-5)^2}=\sqrt{9+16+25}=\sqrt{50}=5\sqrt{2}. \]
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