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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).
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).
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If sum of two unit vector is a unit vector find magnitude of their difference?
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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?.
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?.
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