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If vec a and vec b are unit vectors su...

If ` vec a and vec b` are unit vectors such that `( vec a+ vec b).[(2 vec a+3 vec b)xx(3 vec a-2 vec b)]=0` , then angle between `veca` and ` vec b` is

A

0

B

`pi//2`

C

`pi`

D

indeterminate

Text Solution

Verified by Experts

The correct Answer is:
d
`vec0 = (veca + vecb) . (2veca + 3vecb) xx ( 3veca -2 vecb)`
` = (veca + vecb ) . (-4 veca xx vecb - 9 veca xx vecb)`
`= - 13 (veca + vecb) . (veca xx vecb)`
Which is true for all values of `veca and vecb`.
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CENGAGE PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
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  5. Resolved part of vector veca and along vector vecb " is " veca1 and th...

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  6. vec a=2 hat i- hat j+ hat k , vec b= hat i+2 hat j- hat k , vec c= hat...

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  7. If P is any arbitrary point on the circumcircle of the equilateral t...

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  8. If vec ra n d vec s are non-zero constant vectors and the scalar b...

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  9. vec aa n d vec b are two unit vectors that are mutually perpendicul...

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  10. Given that vec a , vec b , vec p , vec q are four vectors such that ...

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  11. The position vectors of the vertices A ,Ba n dC of a triangle are th...

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  12. If a is real constant A ,B and C are variable angles and sqrt(a^2-4)ta...

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  13. The vertex A triangle A B C is on the line vec r= hat i+ hat j+lambda...

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  14. A non-zero vector vec a is such that its projections along vectors ...

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  15. Position vector hat k is rotated about the origin by angle 135^0 in...

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  16. In a quadrilateral A B C D , vec A C is the bisector of vec A Ba n d ...

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  17. In fig. A B ,D Ea n dG F are parallel to each other and A D ,B Ga n...

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  18. Vector vec a in the plane of vec b=2 hat i+ hat ja n d vec c= hat i-...

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  19. Let A B C D be a tetrahedron such that the edges A B ,A C and A D ar...

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  20. Let vecf(t)=[t] hat i+(t-[t]) hat j+[t+1] hat k , w h e r e[dot] deno...

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