51.
Magnitude of the vector \(2\hat{i}+3\hat{j}+6\hat{k}\) is
Exam Year(s)
Tripura Public Service Commission - 2026,
Answer: D
The magnitude is \(\sqrt{49}\), that is, 7.
The magnitude of a vector is the square root of the sum of the squares of its components:
\[ \begin{aligned} |\vec{v}| &= \sqrt{2^{2} + 3^{2} + 6^{2}} \\ &= \sqrt{4 + 9 + 36} = \sqrt{49} = 7 \end{aligned} \]
√17, √46 and √13 come from leaving out or mis-squaring one of the components; for instance 4 + 9 = 13 drops the 6k term.
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