?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?

Question

?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?

Answer

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

Similar JEE Doubts

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(p^2 q^2 r^2) is equal to * = here is for cross product?

Letbe three non-coplanar unit vectors such that the angle between every pair of them isπ/3 . if where p, q and r are scalars, then the value ofis ___________________ Correct answer is '4'. Can you explain this answer?

If are non-coplanar vectors and l is a real number,then the vectors are non coplanar for

If vector a vector b and vector c are non zero coplaner vectors such that vector a dot vector b equal to vector b dot vector c equal to zero. if magnitude of vector a equqls to 1 units and magnitude of vector c equal to 6 units find the value of magnitude of vector a Dot vector c.?

Top Courses for JEEView all

Physics for JEE Main & Advanced

Mock Tests for JEE Main and Advanced 2025

Mathematics (Maths) for JEE Main & Advanced

Chemistry for JEE Main & Advanced

Chapter-wise Tests for JEE Main & Advanced

Top Courses for JEE

Top Courses for JEE

Suggested Free Tests

Related Content

JEE Courses

Mock Test Series

Past Year Papers

Additional Courses

Company

Similar JEE Doubts

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(p^2 q^2 r^2) is equal to * = here is for cross product?

Letbe three non-coplanar unit vectors such that the angle between every pair of them isπ/3 . if where p, q and r are scalars, then the value ofis ___________________ Correct answer is '4'. Can you explain this answer?

If are non-coplanar vectors and l is a real number,then the vectors are non coplanar for

If vector a vector b and vector c are non zero coplaner vectors such that vector a dot vector b equal to vector b dot vector c equal to zero. if magnitude of vector a equqls to 1 units and magnitude of vector c equal to 6 units find the value of magnitude of vector a Dot vector c.?

Top Courses for JEEView all

Physics for JEE Main & Advanced

Mock Tests for JEE Main and Advanced 2025

Mathematics (Maths) for JEE Main & Advanced

Chemistry for JEE Main & Advanced

Chapter-wise Tests for JEE Main & Advanced

Top Courses for JEE

Top Courses for JEE

Suggested Free Tests

Related Content

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(p^2 q^2 r^2) is equal to * = here is for cross product?