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If veca, vecb and vecc are unit coplanar...

If `veca, vecb and vecc` are unit coplanar vectors , then the scalar triple porduct `[2 veca -vecb" " 2vecb - vecc " "2vecc-veca] `is

A

0

B

1

C

`-sqrt3`

D

`sqrt3`

Text Solution

Verified by Experts

The correct Answer is:
a

`veca vecb and vecc` are unit coplanar vectors, `2veca- vecb , 2vecb - 2vecc and 2vecc - veca` are also coplanar, vectors ], being a linear combination of `veca , vecb and vecc` thus ` [ 2 veca - vecb 2vecb - vecc 2vecc - veca] =0`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. If the vectors veca,vecb,vecc form the sides BC,CA and AB respectively...

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  2. Consider the vectors, vec(a),vec(b),vec(c),vec(d) such that (vec(a)xxv...

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  3. If veca, vecb and vecc are unit coplanar vectors , then the scalar tri...

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  4. If hat a , hat b ,a n d hat c are unit vectors, then | hat a- hat b|^...

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  5. If veca and vecb are two unit vectors such that veca+2vecb and 5veca-4...

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  6. Let vec V=2 hat i+ hat j- hat ka n d vec W= hat i+3 hat kdot If vec ...

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  7. Find the value of a so that the volume of the parallelepiped formed...

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  8. If veca=hati+hatj+hatk, veca.vecb=1 and veca xx vecb = hati-hatk, then...

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  9. The unit vector which is orthogonal to the vector 5hati + 2hatj + 6hat...

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  10. if veca , vecb and vecc are three non-zero, non- coplanar vectors and ...

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  11. Let veca=hati + hatj +hatk,vecb=hati- hatj + hatk and vecc= hati-hatj...

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  12. Let two non-collinear unit vector hat aa n d hat b form an acute a...

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  13. If veca,vecb,vecc and vecd are unit vectors such that (vecaxxvecb).(ve...

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  14. Two adjacent sides of a parallelogram A B C D are given by vec A B=...

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  15. Let P ,Q ,R and S be the points on the plane with position vectors ...

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  16. Let veca=hati + hatj +hatk,vecb=hati- hatj + hatk and vecc= hati-hatj...

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  17. Let bar(PR)=3hati+hatj-2hatk and bar(SQ)=hati-3hatj-4hatk determine d...

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  18. Let veca=a(1)hati+a(2)hatj+a(3)hatk,vecb=b(2)hatj+b(3)hatk and vecc=c(...

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  19. The number of vectors of unit length perpendicular to vectors vec ...

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  20. veca=2hati-hatj+hatk,vecb=hatj+2hatj-hatk,vecc=hati+hatj -2 hatk . A v...

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