Question

\(\left\lVert 3\vec i-4\vec j-5\vec k\right\rVert =\) ?

• A. \(5\sqrt{2}\)
• B. \(12\)
• C. \(2\)
• D. \(9\)

Hint:

Magnitude \(=\sqrt{(\text{x-part})^2+(\text{y-part})^2+(\text{z-part})^2}\).

Answer 1

The Correct Option is A

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. \[ \sqrt{3^2+(-4)^2+(-5)^2}=\sqrt{9+16+25}=\sqrt{50}=5\sqrt{2}. \]