Q73 / 160 · AP EAMCET 2021 (20 Aug Shift 2) · Mathematics

Let $\vec{u}$ and $\vec{v}$ be two non-zero vectors with the intermediate angle $45 °$ . Then $| \vec{u} \times \vec{v} | =$

Solution

Given that, $θ = 45^{ο}$

As we know that $| \vec{u} \times \vec{v} | = |\vec{u}| |\vec{v}| \sin θ & \vec{u} \cdot \vec{v} = |\vec{u}| |\vec{v}| \cos θ$

$| \vec{u} \times \vec{v} | = |\vec{u}| |\vec{v}| \sin 45^{ο}$

$\Rightarrow | \vec{u} \times \vec{v} | = \frac{|\vec{u}| |\vec{v}|}{\sqrt{2}}$

$\Rightarrow | \vec{u} \times \vec{v} | = |\vec{u}| |\vec{v}| \cos 45^{ο}$

$\Rightarrow | \vec{u} \times \vec{v} | = \vec{u} \cdot \vec{v}$

Hence, the correct answer is option: 'C'.