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If veca and vecb are unit vectors such t...

If `veca and vecb` are unit vectors such that `(veca +vecb). (2veca + 3vecb)xx(3veca - 2vecb)=vec0` then angle between `veca and vecb` 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-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
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  2. Given three vectors eveca, vecb and vecc two of which are non-collinea...

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  3. If veca and vecb are unit vectors such that (veca +vecb). (2veca + 3ve...

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  6. Let veca=2hati=hatj+hatk, vecb=hati+2hatj-hatk and vecc=hati+hatj-2hat...

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  7. If P is any arbitrary point on the circumcirlce of the equllateral ...

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  9. veca and vecb are two unit vectors that are mutually perpendicular. A...

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  10. Given that veca,vecb,vecp,vecq are four vectors such that veca + vecb...

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

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  12. If a is real constant A ,Ba n dC 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 i...

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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. 2.33 AB, DE and GF are parallel to each other and AD, BG and E...

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  18. A unit vector veca in the plane of vecb=2hati+hatj and vecc=hati-hatj+...

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  19. Let A B C D be a tetrahedron such that the edges A B ,A Ca n dA D a...

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