First slide

Vectors

Question

If F₁ and F₂ are two vectors of equal magnitudes F such that I F₁ . F₂ I= I $F_{1}$ X F₂|, then IF₁ + F₂| equals to

Moderate

A

$\sqrt{(2 + \sqrt{2)}} F$
B

2F
C

$F \sqrt{2}$
D

None of these

Solution

$F \cdot F \cos θ = F \cdot F \sin θ or \tan θ = 1 or θ = 45 °$
$|F_{1} + F_{2}| = \sqrt{F^{2} + F^{2} + 2 F \cdot F \cos 45 °} = (\sqrt{2 + \sqrt{2}}) F$

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