Two vectors overrightarrow{a} and overrightar | vedclass

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

Question

(B) The angle between the vectors is $	heta = 60^{\circ}$.The angle between the resultant vector and $\vec{a}$ is $\phi = 45^{\circ}$.According to th

Vedclass · Accepted Answer

$\sqrt{3}-1$

Vedclass · Answer

(B) The angle between the vectors is $	heta = 60^{\circ}$.The angle between the resultant vector and $\vec{a}$ is $\phi = 45^{\circ}$.According to the parallelogram law of vector addition,the angle $\phi$ that the resultant makes with vector $\vec{a}$ is given by:$	an(\phi) = \frac{|\vec{b}| \sin(	heta)}{|\vec{a}| + |\vec{b}| \cos(	heta)}$Substituting the given values $|\vec{b}| = 2$,$	heta = 60^{\circ}$,and $\phi = 45^{\circ}$:$	an(45^{\circ}) = \frac{2 \sin(60^{\circ})}{|\vec{a}| + 2 \cos(60^{\circ})}$Since $	an(45^{\circ}) = 1$,$\sin(60^{\circ}) = \frac{\sqrt{3}}{2}$,and $\cos(60^{\circ}) = \frac{1}{2}$:$1 = \frac{2 	imes (\frac{\sqrt{3}}{2})}{|\vec{a}| + 2 	imes (\frac{1}{2})}$$1 = \frac{\sqrt{3}}{|\vec{a}| + 1}$$|\vec{a}| + 1 = \sqrt{3}$$|\vec{a}| = \sqrt{3} - 1$ units.

Two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are at an angle of $60^{\circ}$ with each other. Their resultant makes an angle of $45^{\circ}$ with $\overrightarrow{a}$. If $|\vec{b}|=2$ units,then $|\vec{a}|$ is

Similar Questions

Two vectors of equal magnitude $5$ units have an angle $60^\circ$ between them. Find the magnitude of $(a)$ the sum of the vectors and $(b)$ the difference of the vectors.

The magnitude of the vector sum of two forces $10 \ N$ and $6 \ N$ cannot be ......... $N$.

Two forces $F_1 = 3 \ N$ at $0^o$ and $F_2 = 5 \ N$ at $60^o$ act on a body. Then a single force that would balance the two forces must have a magnitude of .......... $N$

If the sum of two unit vectors is a unit vector,find the magnitude of their difference.

Two forces of magnitude $8 \, N$ and $15 \, N$ respectively act at a point. If the resultant force is $17 \, N$,the angle between the forces is: (in $^{\circ}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module