The sum of two forces P ⃗ and Q ⃗ is R ⃗ such that | R ⃗ | = | P ⃗ | . The angle θ (in degrees) that the resultant of 2 P ⃗ and Q ⃗ will make with Q ⃗ is,

| P ? + Q ? | = | P ? | P 2 + Q 2 + 2 P Q c o s ? θ = P 2 ⇒ Q + 2 P c o s ? θ = 0 ⇒ c o s ? θ = - Q 2 P t a n ? α = 2 P s i n ? θ 2 P c o s ? θ + Q = ∞ ? [ 2 P c o s ? θ + Q = 0 ] α = 90 ?

The sum of two forces $\vec{P}$ and $\vec{Q}$ is $\vec{R}$ such that $| \vec{R} | = | \vec{P} |$ . The angle $θ$ (in degrees) that the resultant of $2 \vec{P}$ and $\vec{Q}$ will make with $\vec{Q}$ is,

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Alok Kumar Singh | Contributor-Level 10

6 months ago

$| \overset{?}{P} + \overset{?}{Q} | = | \overset{?}{P} |$

^{$P^{2} + Q^{2} + 2 P Q c o s ? θ = P^{2}$}

$\Rightarrow Q + 2 P c o s ? θ = 0$

$\Rightarrow c o s ? θ = - \frac{Q}{2 P}$

$t a n ? α = \frac{2 P s i n ? θ}{2 P c o s ? θ + Q} = \infty$

$? [2 P c o s ? θ + Q = 0]$

α = 90^{?}

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