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If the vectors 3 vec p + vec q; 5 vec p ...

If the vectors `3 vec p + vec q`; `5 vec p - 3 vecq` and `2 vec p + vec q`; `4 vec p - 2 vec q` are pairs of mutually perpendicular then sin( `vec p` ^ `vec q)` is :

A

`(sqrt(55))/(4)`

B

`(sqrt(55))/(8)`

C

`(3)/(16)`

D

`(sqrt(247))/(16)`

Text Solution

Verified by Experts

The correct Answer is:
B
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ARIHANT MATHS-PRODUCT OF VECTORS-Exercise (Single Option Correct Type Questions)
  1. The values of x for which the angle between the vectors veca = xhati -...

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  2. If a, b and c are non-coplanar vectors and d=lambdaa+mub+nuc, then lam...

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  3. If the vectors 3 vec p + vec q; 5 vec p - 3 vecq and 2 vec p + vec q; ...

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  4. Let vec u=hat i+hat j,vec v=hat i-hat j and vec w=hat i+2 hat j+3hat k...

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  5. Given a parallelogram ABCD. If |vec(AB)|=a, |vec(AD)| = b & |vec(AC)| ...

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  6. For two particular vectors vec A and vec B it is known that vec A xx ...

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  7. For some non zero vector barV, if the sum of bar V and the vector obta...

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  8. In isosceles triangles A B C ,| vec A B|=| vec B C|=8, a point E divid...

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  9. Given an equilateral triangle ABC with side length equal to 'a'. Let M...

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  10. In a quadrilateral ABCD, AC is the bisector of the (AB, AD) which is (...

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  11. If the distance from the point P(1, 1, 1) to the line passing through ...

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  12. Given the vectors vec u=2 hat i-hat j-hat k and vec v=hat i-hat j+2ha...

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  13. Vector vec c is perpendicular to vectors vec a=(2,-3,1)a n d vec ...

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  14. Let vec a= hat j+hat j,vec b=hat j+hat k and vec c=alpha vec a+beta v...

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  15. A rigid body rotates about an axis through the origin with an angular ...

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  16. A rigid body rotates with constant angular velocity omaga about the li...

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  17. Consider DeltaABC with A=(veca);B=(vecb) and C=(vecc). If vecb.(veca+v...

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  18. Given unit vectors m, n and p such that angle between m and n. Angle b...

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  19. If veca and vecb are two unit vectors, then the vector (veca+vecb)xx(v...

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  20. If veca and vecb are othogonal unit vectors, then for a vector vecr no...

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