Let vec{u} and vec{v} be two non-zero vectors | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The magnitude of the cross product of two vectors $\vec{u}$ and $\vec{v}$ is given by $|\vec{u} 	imes \vec{v}| = |\vec{u}||\vec{v}| \sin 	heta$,

Vedclass · Accepted Answer

$\vec{u} \cdot \vec{v}$

Vedclass · Answer

(C) The magnitude of the cross product of two vectors $\vec{u}$ and $\vec{v}$ is given by $|\vec{u} 	imes \vec{v}| = |\vec{u}||\vec{v}| \sin 	heta$,where $	heta$ is the angle between them.Given $	heta = 45^{\circ}$,we have $|\vec{u} 	imes \vec{v}| = |\vec{u}||\vec{v}| \sin 45^{\circ} = |\vec{u}||\vec{v}| \left( \frac{1}{\sqrt{2}} ight)$.The dot product of the two vectors is given by $\vec{u} \cdot \vec{v} = |\vec{u}||\vec{v}| \cos 	heta$.For $	heta = 45^{\circ}$,$\vec{u} \cdot \vec{v} = |\vec{u}||\vec{v}| \cos 45^{\circ} = |\vec{u}||\vec{v}| \left( \frac{1}{\sqrt{2}} ight)$.Since $\sin 45^{\circ} = \cos 45^{\circ} = \frac{1}{\sqrt{2}}$,it follows that $|\vec{u} 	imes \vec{v}| = \vec{u} \cdot \vec{v}$.

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

Similar Questions

If three vectors $a, b, c$ satisfy $a + b + c = 0$ and $|a| = 3, |b| = 5, |c| = 7,$ then the angle between $a$ and $b$ is .............. $^o$

If $\bar{a}$ and $\bar{b}$ are two unit vectors such that $\bar{a}+2 \bar{b}$ and $5 \bar{a}-4 \bar{b}$ are perpendicular to each other,then the angle between $\bar{a}$ and $\bar{b}$ is

If $\overline{a}$ and $\overline{b}$ are two unit vectors such that $\overline{a}+2\overline{b}$ and $5\overline{a}-4\overline{b}$ are perpendicular to each other,then the angle between $\overline{a}$ and $\overline{b}$ is

If $a, b$ and $c$ are unit vectors such that $a+b+c=0$,then $a \cdot b+b \cdot c+c \cdot a$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module