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The sum of two unit vectors is a unit vector. The difference of the two unit vectors is of magnitude ?
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Explanation of Sum and Difference of Unit Vectors
Sum of Two Unit Vectors
Let us assume that two unit vectors are represented by a and b, then their sum is:
a + b = c
As per the question, c is also a unit vector:
|c| = 1
Therefore, we can write:
|a + b| = 1
Squaring both sides:
(a + b) . (a + b) = 1
Expanding the equation:
|a|² + 2a . b + |b|² = 1
Since a and b are unit vectors, we can write:
|a|² + 2a . b + |b|² = 1 + 1
Or,
2 + 2a . b = 2
Therefore, a . b = 0
This shows that the two unit vectors are perpendicular to each other.
Difference of Two Unit Vectors
Let us assume that two unit vectors are represented by a and b, then their difference is:
a - b = c
As per the question, we need to find the magnitude of c:
|c| = |a - b|
Using the distance formula, we can write:
|a - b| = √[(a₁-b₁)² + (a₂-b₂)² + (a₃-b₃)²]
As both a and b are unit vectors, their magnitude is 1:
Therefore,
|a - b| = √[(1-1)² + (1-1)² + (1-1)²]
Or,
|a - b| = √[0] = 0
Therefore, the magnitude of the difference of two unit vectors is 0.
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The sum of two unit vectors is a unit vector. The difference of the two unit vectors is of magnitude ?
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The sum of two unit vectors is a unit vector. The difference of the two unit vectors is of magnitude ? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The sum of two unit vectors is a unit vector. The difference of the two unit vectors is of magnitude ? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of two unit vectors is a unit vector. The difference of the two unit vectors is of magnitude ?.
The sum of two unit vectors is a unit vector. The difference of the two unit vectors is of magnitude ? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The sum of two unit vectors is a unit vector. The difference of the two unit vectors is of magnitude ? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of two unit vectors is a unit vector. The difference of the two unit vectors is of magnitude ?.
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