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

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

Question

(B) Let $\vec{a}$ and $\vec{b}$ be two unit vectors such that their sum $\vec{c} = \vec{a} + \vec{b}$ is also a unit vector.Given $|\vec{a}| = 1$,$|\v

Vedclass · Accepted Answer

$\sqrt{3}$

Vedclass · Answer

(B) Let $\vec{a}$ and $\vec{b}$ be two unit vectors such that their sum $\vec{c} = \vec{a} + \vec{b}$ is also a unit vector.Given $|\vec{a}| = 1$,$|\vec{b}| = 1$,and $|\vec{a} + \vec{b}| = 1$.Squaring the magnitude of the sum: $|\vec{a} + \vec{b}|^2 = |\vec{a}|^2 + |\vec{b}|^2 + 2(\vec{a} \cdot \vec{b}) = 1^2$.Substituting the values: $1 + 1 + 2(\vec{a} \cdot \vec{b}) = 1$,which gives $2(\vec{a} \cdot \vec{b}) = -1$,so $\vec{a} \cdot \vec{b} = -1/2$.Now,the magnitude of their difference is $|\vec{a} - \vec{b}| = \sqrt{|\vec{a}|^2 + |\vec{b}|^2 - 2(\vec{a} \cdot \vec{b})}$.Substituting the values: $|\vec{a} - \vec{b}| = \sqrt{1 + 1 - 2(-1/2)} = \sqrt{1 + 1 + 1} = \sqrt{3}$.

If the sum of two unit vectors is a unit vector,what is the magnitude of their difference?

Similar Questions

$\int_0^\pi \frac{\theta \sin \theta}{1+\cos ^2 \theta} d \theta$ is equal to

$H^{+}$,$D^{+}$,and $T^{+}$ differ in all of the following $EXCEPT$ one. Identify it.

Which of the following molecules does not have a linear arrangement of atoms?

Cuscuta is an example of

Which one of the following types of organisms occupy more than one trophic level in a pond ecosystem?

Vedclass Test Series

Exam Paper Generator

Online Exam Module