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3-1.Vectors
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If $F _1$ and $F _2$ are two vectors of equal magnitudes $F$ such that $\left| F _1 \cdot F _2\right|=\left| F _1 \times F _2\right|$, then $\left| F _1+ F _2\right|$ equals to
A$\sqrt{(2+\sqrt{2)}} F$
B$2 F$
C$F \sqrt{2}$
DNone of these
Solution
(a) $F \cdot F \cdot \cos \theta =F \cdot F \cdot \sin \theta \text { or } \tan \theta=1 \text { or } \theta=45^{\circ}$
$\left| F _1+ F _2\right| =\sqrt{F^2+F^2+2 \cdot F \cdot F \cdot \cos 45^{\circ}} ~\\ =(\sqrt{2+\sqrt{2}}) F$
$\left| F _1+ F _2\right| =\sqrt{F^2+F^2+2 \cdot F \cdot F \cdot \cos 45^{\circ}} ~\\ =(\sqrt{2+\sqrt{2}}) F$
Standard 11
Physics