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Question Number 213045 by MrGaster last updated on 29/Oct/24
a^⇀ ,b^⇀ ls the unit vector,∣a^⇀ +b^⇀ ∣=1  ask ∣a^⇀ −b^⇀ ∣?
$$\overset{\rightharpoonup} {{a}},\overset{\rightharpoonup} {{b}ls}\:{the}\:{unit}\:{vector},\mid\overset{\rightharpoonup} {{a}}+\overset{\rightharpoonup} {{b}}\mid=\mathrm{1} \\ $$$${ask}\:\mid\overset{\rightharpoonup} {{a}}−\overset{\rightharpoonup} {{b}}\mid? \\ $$
Answered by mr W last updated on 29/Oct/24
Commented by mr W last updated on 29/Oct/24
∣a^(→) +b^(→) ∣=(√(1^2 +1^2 −1×1))=1  ∣a^(→) −b^(→) ∣=(√(1^2 +1^2 +1×1))=(√3) ✓
$$\mid\overset{\rightarrow} {\boldsymbol{{a}}}+\overset{\rightarrow} {\boldsymbol{{b}}}\mid=\sqrt{\mathrm{1}^{\mathrm{2}} +\mathrm{1}^{\mathrm{2}} −\mathrm{1}×\mathrm{1}}=\mathrm{1} \\ $$$$\mid\overset{\rightarrow} {\boldsymbol{{a}}}−\overset{\rightarrow} {\boldsymbol{{b}}}\mid=\sqrt{\mathrm{1}^{\mathrm{2}} +\mathrm{1}^{\mathrm{2}} +\mathrm{1}×\mathrm{1}}=\sqrt{\mathrm{3}}\:\checkmark \\ $$
Commented by MrGaster last updated on 29/Oct/24
Thank you,sir.
$${Thank}\:{you},{s}\mathrm{i}{r}. \\ $$

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