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Let a, b, c be non coplanar unit vectors, making an angle of 60º with each other. If a* b b* c =pa qb rc then the value of 2(p2 q2 r2) is equal t?
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?Let a, b, c be non coplanar unit vectors, making an angle of 60º with...
Solution
Given
a, b, c are non-coplanar unit vectors making an angle of 60º with each other.
a * b * c = paqbrc
To Find
The value of 2(p2 + q2 + r2)
Explanation
Let’s first calculate a * b and b * c.
a * b = |a| |b| cos(60º) = (1)(1)(1/2) = 1/2
b * c = |b| |c| cos(60º) = (1)(1)(1/2) = 1/2
Now, we can write a * b * c as:
a * b * c = (a * b) * c = (1/2) * c = c/2
Since a, b, and c are unit vectors, we can say that:
|a * b * c| = |c/2| = 1/2
Also, we are given that:
a * b * c = paqbrc
So, we can say that:
|paqbrc| = |c/2| = 1/2
Therefore, |p| |q| |r| = 1
Now, we have to find the value of 2(p2 + q2 + r2).
Let’s first find the value of (p2 + q2 + r2).
We know that |p| |q| |r| = 1.
So, we can write:
p2 q2 r2 = 1
p2 + q2 + r2 = 1/(p2 r2)
Now, we have to find the value of 2/(p2 r2).
We know that:
2/(p2 r2) = (p2 r2 + q2 r2 + p2 q2)/(p2 r2)
2/(p2 r2) = (p2 r2)/(p2 r2) + (q2 r2)/(p2 r2) + (p2 q2)/(p2 r2)
2/(p2 r2) = 1 + (q2 r2)/(p2 r2) + (p2 q2)/(p2 r2)
2/(p2 r2) = 1 + (q/p)2 + (r/p)2
2(p2 + q2 + r2) = 2p2 + 2(q/p)2p2 + 2(r/p)2p2
2(p2 + q2 + r2) = 2p2(1 + (q/p)2 + (r/p)2)
2(p2 + q2 + r2) = 2
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?Let a, b, c be non coplanar unit vectors, making an angle of 60º with each other. If a* b b* c =pa qb rc then the value of 2(p2 q2 r2) is equal t?
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?Let a, b, c be non coplanar unit vectors, making an angle of 60º with each other. If a* b b* c =pa qb rc then the value of 2(p2 q2 r2) is equal t? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about ?Let a, b, c be non coplanar unit vectors, making an angle of 60º with each other. If a* b b* c =pa qb rc then the value of 2(p2 q2 r2) is equal t? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ?Let a, b, c be non coplanar unit vectors, making an angle of 60º with each other. If a* b b* c =pa qb rc then the value of 2(p2 q2 r2) is equal t?.
?Let a, b, c be non coplanar unit vectors, making an angle of 60º with each other. If a* b b* c =pa qb rc then the value of 2(p2 q2 r2) is equal t? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about ?Let a, b, c be non coplanar unit vectors, making an angle of 60º with each other. If a* b b* c =pa qb rc then the value of 2(p2 q2 r2) is equal t? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ?Let a, b, c be non coplanar unit vectors, making an angle of 60º with each other. If a* b b* c =pa qb rc then the value of 2(p2 q2 r2) is equal t?.
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