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Find the volume of a parallelepiped whose edges are given by `3 hat i+7 hat j-5 hat k ,5 hat i+7 hat j-` 3` hat k` and `7 hat i-5 hat j-3 hat k`

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Given that,
`vec a =3 hat i+7 hat j-5 hat k`
`vec b =5 hat i+7 hat j-3 hat k`
`vec c =7 hat i-5 hat j-3 hat k`

`V= |vec a.(vec b times vec c)|`
`V=|(3, 7, -5), (5, 7, -3), (7, -5, -3)|`
`V=3(21-15)-7(-15+21)-5(-25-49)`
`V=18-42+370`
...
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RD SHARMA-SCALAR TRIPLE PRODUCT -Solved Examples And Exercises
  1. Let vec a= hat i+ hat j+ hat k , vec b= hat i and hat c=c1 hat i+c2...

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  2. Find [ vec a , vec b , vec c],when vec a=2 hat i-3 hat j+4 hat k , vec...

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  3. Find the volume of a parallelepiped whose edges are given by 3 hat i...

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  4. If |(a,a^2, 1+a^3),(b,b^2, 1+b^3),(c,c^2, 1+c^3)|=0 and the vectors v...

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  5. Evaluate [ hat i hat j hat k][ hat i hat k hat j]

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  6. Simplify: [ vec a- vec b, vec b- vec c, vec c- vec a]

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  7. If the vectors vecalpha=a hat i+a hat j+c hat k , vecbeta= hat i+ hat...

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  8. Determine alpha such that a vector vec r is at right angles to each o...

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  9. Find the range of f(x)= sin^-1x+tan^-1x+cos^-1x

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  10. For any three vectors a b,c, show that vec a xx (vec b +vec c)+vec b x...

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  11. Let vec a , vec b , vec c be three non-zero vectors such that vec c ...

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  12. Let vec a , vec ba n d vec c , be non-zero non-coplanar vectors. Prov...

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  13. Find the altitude of a parallelepiped determined by the vectors ve...

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  14. Let vec a , vec b , vec c , be three non-zero vectors. If vec adot( ...

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  15. If a is a non-zero real number, then prove that the vectors vecalp...

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  16. If vec a+vec b+vec c=0, prove that (vec a xx vec b)=(vec b xx vec c)=(...

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  17. Show that the vectors vec a=-2 hat i-2 hat j+4 hat k ,\ vec b=-2 ...

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  18. Find lambda so that the vectors vec a=2 hat i- hat j+ hat k ,\ vec b...

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  19. The four points whose position vector are 6 hat i - 7 hat j,16 hat i -...

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  20. For any three vectors a ,\ b ,\ c prove that [ vec a+ vec b\ vec b...

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