If P × Q = Q × P, the angle between P and Q is θ(0° < θ < 360 °). The value of ' θ ' will be ___________ °. Numerical answer type. Work it out, then open the answer.

Answer: 180. Q × P = -P × Q, so the condition gives 2P × Q = 0. PQsin θ = 0 ⇒ sin θ = 0. In 0° < θ < 360° the only value is θ = 180°. So θ = 180°.

If P × Q = Q × P, the angle between P and Q is θ(0° < θ < 360 °). The… | JEE Main 2021 (25 Feb, Shift 2)

Q11JEE Main 2021 · 25 FEB · SHIFT 2Easy

Vector (Cross) Product

If $\vec{P} \times \vec{Q} = \vec{Q} \times \vec{P}$ , the angle between $\vec{P}$ and $\vec{Q}$ is $\theta(0^\circ$ < $\theta$ < 360 $^\circ$ ). The value of ' $\theta$ ' will be ___________ $^\circ$ .

Numerical answer type. Work it out, then open the answer.

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Answer: 180

$\vec{Q} \times \vec{P} = -\vec{P} \times \vec{Q}$ , so the condition gives $2\vec{P} \times \vec{Q} = 0$ .
$PQ\sin\theta = 0 \Rightarrow \sin\theta = 0$ .
In $0^\circ < \theta < 360^\circ$ the only value is $\theta = 180^\circ$ .
So $\theta = 180^\circ$ .

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