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If the volume of a parallelepiped who...

If the volume of a parallelepiped whose adjacent edges are ` vec a=2 hat i+3 hat j+4 hat k , vec b= hat i+alpha hat j+2 hat k , vec c= hat i+2 hat j+alpha hat k` is 15, then find the value of `alpha` if `(alpha>0)dot`

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CENGAGE PUBLICATION-VECTOR ALGEBRA-All Questions
  1. Let vec a=a1 hat i+a2 hat j+a3 hat k , vec b=b1 hat i+b2 hat j+b3 hat...

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  2. Statement 1: vec a , vec b ,a n d vec c are three mutually perpendi...

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  3. If the volume of a parallelepiped whose adjacent edges are vec a=2...

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  4. Prove that [ vec l vec m vec n][ vec a vec b vec c]=| (vec l. vec a, v...

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  5. Using dot product of vectors, prove that a parallelogram, whose dia...

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  6. If a+2b+3c=4, then find the least value (to the nearest integer) of ...

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  7. In any triangle A B C , prove the projection formulaa=b cosC+c cosB ...

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  8. Prove that an angle inscribed in a semi-circle is a right angle usi...

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  9. If vec a.hat i= vec a.( hat i+ hat j)= vec a.( hat i+ hat j+ hat k) ...

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  10. Prove by vector method that cos(A+B)=cos AcosB-sinAsinBdot

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  11. If the scalar projection of vector x hat i- hat j+ hat k on vector 2...

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  12. If vec a=x hat i+(x-1) hat j+ hat k and vec b=(x+1) hat i+ hat j+a ha...

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  13. A unit vector a makes an angle pi/ 4 with z-axis. If a + i + j is a un...

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  14. if veca, vecb and vecc are there mutually perpendicular unit vectors a...

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  15. If vec a , vec b , and vec c be non-zero vectors such that no two ...

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  16. If vec p , vec q , vec r denote vector vec bxx vec c , vec cxx vec a...

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  17. If vec a and vec b be two non-collinear unit vector such that vec ...

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  18. Show that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b)dot

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  19. Prove that ( vec a.( vec bxx hat i)) hat i+( vec a.( vec bxx hat j)) h...

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  20. For any four vectors, vec a , vec b , vec c and vec d prove that vec...

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