UPSC Exam  >  UPSC Questions  >  If sum of two unit vector is a unit vector fi... Start Learning for Free
If sum of two unit vector is a unit vector find magnitude of their difference?
Most Upvoted Answer
If sum of two unit vector is a unit vector find magnitude of their dif...
Explanation:

Given:
Let u and v be two unit vectors, such that |u + v| = 1

Concept:
The magnitude of the difference of two vectors can be found using the formula:
|u - v| = sqrt(|u|^2 + |v|^2 - 2|u||v|cos(θ))
where θ is the angle between the two vectors.

Derivation:
Given that |u + v| = 1, we have:
|u|^2 + |v|^2 + 2|u||v|cos(θ) = 1
Since u and v are unit vectors, |u| = |v| = 1
Substitute the values in the equation:
1 + 2cos(θ) = 1
cos(θ) = 0
θ = π/2
Substitute θ = π/2 in the formula:
|u - v| = sqrt(1 + 1 - 2*1*1*cos(π/2))
|u - v| = sqrt(2)
Therefore, the magnitude of the difference of the two unit vectors u and v is sqrt(2).
Explore Courses for UPSC exam

Top Courses for UPSC

If sum of two unit vector is a unit vector find magnitude of their difference?
Question Description
If sum of two unit vector is a unit vector find magnitude of their difference? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If sum of two unit vector is a unit vector find magnitude of their difference? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If sum of two unit vector is a unit vector find magnitude of their difference?.
Solutions for If sum of two unit vector is a unit vector find magnitude of their difference? in English & in Hindi are available as part of our courses for UPSC. Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of If sum of two unit vector is a unit vector find magnitude of their difference? defined & explained in the simplest way possible. Besides giving the explanation of If sum of two unit vector is a unit vector find magnitude of their difference?, a detailed solution for If sum of two unit vector is a unit vector find magnitude of their difference? has been provided alongside types of If sum of two unit vector is a unit vector find magnitude of their difference? theory, EduRev gives you an ample number of questions to practice If sum of two unit vector is a unit vector find magnitude of their difference? tests, examples and also practice UPSC tests.
Explore Courses for UPSC exam

Top Courses for UPSC

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev