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VECTOR ALGEBRA — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVECTOR ALGEBRA1 Mark
Question
State True or False for the following:
If $|\vec{\text{a}}|=|\vec{\text{b}}|,$ then necessarily it implies $\vec{\text{a}}=\pm\vec{\text{b}}.$
✓

Answer

False.Solution:
Consider $\vec{\text{a}}=2\hat{\text{i}}+2\hat{\text{j}}-2\hat{\text{k}}$ and $\vec{\text{b}}=2\hat{\text{i}}-\hat{\text{j}}-2\hat{\text{k}}$
Clearly $|\vec{\text{a}}|=|\vec{\text{b}}|,$ but $\vec{\text{a}}=\pm\vec{\text{b}}$
So, the given statement false.

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