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If the difference of two unit vectors is a unit vector, then the magnitude of there sum is : (a) 1/√2 (b) √2 (c) 1/√3 (d) √3
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If the difference of two unit vectors is a unit vector, then the magni...
By triangle Its will be equilateral as all side are equal so angle between 2 sides will be 60 By sum of vector formula A+B= √[A^2 +B^2 +2AB cosQ] Q=60, A=B=1SO SUM of vector will be √(1+1+2x1/2)=√3According to me this should be the answer, let me know if there is anything wrong...
Community Answer
If the difference of two unit vectors is a unit vector, then the magni...
Solution:
Let u and v be two unit vectors such that |u - v| = 1.
We need to find |u + v|.
Proof:
Step 1: Finding the dot product of u and v.
Let's take the dot product of u and v.
u.v = |u||v|cosθ
Since u and v are unit vectors, |u| = |v| = 1.
Thus,
u.v = cosθ
Step 2: Finding u + v.
Now, let's consider u + v.
|u + v|^2 = (u + v).(u + v)
= u.u + 2u.v + v.v
= |u|^2 + |v|^2 + 2u.v
= 2 + 2cosθ [since |u| = |v| = 1]
Step 3: Finding the value of cosθ.
We know that |u - v| = 1.
|u - v|^2 = (u - v).(u - v)
= u.u - 2u.v + v.v
= 2 - 2cosθ [since |u| = |v| = 1]
|u - v|^2 = 1
=> 2 - 2cosθ = 1
=> cosθ = 1/2
Step 4: Finding |u + v|.
Putting the value of cosθ in step 2, we get
|u + v|^2 = 2 + 2(1/2)
= 3
=> |u + v| = sqrt(3)
Therefore, the correct option is (d) sqrt(3).
Let u and v be two unit vectors such that |u - v| = 1.
We need to find |u + v|.
Proof:
Step 1: Finding the dot product of u and v.
Let's take the dot product of u and v.
u.v = |u||v|cosθ
Since u and v are unit vectors, |u| = |v| = 1.
Thus,
u.v = cosθ
Step 2: Finding u + v.
Now, let's consider u + v.
|u + v|^2 = (u + v).(u + v)
= u.u + 2u.v + v.v
= |u|^2 + |v|^2 + 2u.v
= 2 + 2cosθ [since |u| = |v| = 1]
Step 3: Finding the value of cosθ.
We know that |u - v| = 1.
|u - v|^2 = (u - v).(u - v)
= u.u - 2u.v + v.v
= 2 - 2cosθ [since |u| = |v| = 1]
|u - v|^2 = 1
=> 2 - 2cosθ = 1
=> cosθ = 1/2
Step 4: Finding |u + v|.
Putting the value of cosθ in step 2, we get
|u + v|^2 = 2 + 2(1/2)
= 3
=> |u + v| = sqrt(3)
Therefore, the correct option is (d) sqrt(3).
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If the difference of two unit vectors is a unit vector, then the magnitude of there sum is : (a) 1/√2 (b) √2 (c) 1/√3 (d) √3
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If the difference of two unit vectors is a unit vector, then the magnitude of there sum is : (a) 1/√2 (b) √2 (c) 1/√3 (d) √3 for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If the difference of two unit vectors is a unit vector, then the magnitude of there sum is : (a) 1/√2 (b) √2 (c) 1/√3 (d) √3 covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the difference of two unit vectors is a unit vector, then the magnitude of there sum is : (a) 1/√2 (b) √2 (c) 1/√3 (d) √3.
If the difference of two unit vectors is a unit vector, then the magnitude of there sum is : (a) 1/√2 (b) √2 (c) 1/√3 (d) √3 for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If the difference of two unit vectors is a unit vector, then the magnitude of there sum is : (a) 1/√2 (b) √2 (c) 1/√3 (d) √3 covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the difference of two unit vectors is a unit vector, then the magnitude of there sum is : (a) 1/√2 (b) √2 (c) 1/√3 (d) √3.
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