If the sum of two unit vectors is also a unit | vedclass

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

Question

(B) Let the two unit vectors be $\vec{A}$ and $\vec{B}$,where $|\vec{A}| = 1$ and $|\vec{B}| = 1$.Given that their sum $\vec{R} = \vec{A} + \vec{B}$ i

Vedclass · Accepted Answer

$\sqrt{3}, 120^{\circ}$

Vedclass · Answer

(B) Let the two unit vectors be $\vec{A}$ and $\vec{B}$,where $|\vec{A}| = 1$ and $|\vec{B}| = 1$.Given that their sum $\vec{R} = \vec{A} + \vec{B}$ is also a unit vector,so $|\vec{R}| = 1$.The magnitude of the resultant vector is given by $|\vec{R}| = \sqrt{A^2 + B^2 + 2AB \cos 	heta} = 1$.Squaring both sides: $1^2 + 1^2 + 2(1)(1) \cos 	heta = 1^2$.$2 + 2 \cos 	heta = 1 \Rightarrow 2 \cos 	heta = -1 \Rightarrow \cos 	heta = -1/2$.Thus,the angle $	heta = 120^{\circ}$.Now,the magnitude of their difference is $|\vec{A} - \vec{B}| = \sqrt{A^2 + B^2 - 2AB \cos 	heta}$.Substituting the values: $|\vec{A} - \vec{B}| = \sqrt{1^2 + 1^2 - 2(1)(1) \cos 120^{\circ}}$.Since $\cos 120^{\circ} = -1/2$,we get $|\vec{A} - \vec{B}| = \sqrt{1 + 1 - 2(-1/2)} = \sqrt{1 + 1 + 1} = \sqrt{3}$.Therefore,the magnitude of the difference is $\sqrt{3}$ and the angle is $120^{\circ}$.

If the sum of two unit vectors is also a unit vector,then the magnitude of their difference and the angle between the two given unit vectors is ..............

Similar Questions

Two forces of $10 \,N$ and $6 \,N$ act upon a body. The directions of the forces are unknown. The resultant force on the body may be .........$N$.

The sum of the magnitudes of two forces acting at a point is $16 \,N$. If their resultant is normal to the smaller force and has a magnitude of $8 \,N$, then the forces are:

There are five vectors,each of magnitude $8$ units. These vectors form a regular pentagon as shown in the figure. Find the magnitude of the resultant vector.

Write two properties of vector addition.

Maximum and minimum magnitudes of the resultant of two vectors of magnitudes $P$ and $Q$ are in the ratio $3:1.$ Which of the following relations is true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module