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Find the value of lambda if the volume o...

Find the value of `lambda` if the volume of a tetrahedron whose vertices are with position vectors ` hat i-6 hat j+10 hat k ,- hat i-3 hat j+7 hat k ,5 hat i- hat j+lambda hat k and 7 hat i-4 hat j+7 hat k` is 11 cubic unit.

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Find the value of lambda for which the three points with position vector 3 hat i-2 hat j- hat k ,2 hat i+3 hat j-4 hat k , and4 hat i+5 hat j+lambda hat k are coplanar.

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CENGAGE PUBLICATION-VECTOR ALGEBRA-All Questions
  1. If hat a , hat b ,a n d hat c are unit vectors, then | hat a-hat b|^2...

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  2. Which of the following expressions are meaningful? a. vec u.(vec vx...

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  3. Find the value of lambda if the volume of a tetrahedron whose vertic...

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  4. Let vec a=2 hat i- hat j+ hat k , vec b= hat i+2 hat j= hat ka n d ve...

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  5. If ( vec axx vec b)xx( vec cxx vec d).( vec axx vec d)=0 , then which ...

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  6. Vector 1/3(2hati-2hatj+hatk) is (A) a unit vector (B) makes an angle ...

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  7. Let vec u and vec v be unit vectors such that vec uxx vec v+ vec u= ...

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  8. The scalars l and m such that l vec a+m vec b= vec c ,where vec a , v...

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  9. If O A B C is a tetrahedron where O is the origin and A ,B ,a n dC are...

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  10. If K is the length of any edge of a regular tetrahedron, then the dist...

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  11. In triangle A B C , a point P is taken on A B such that A P//B P=1//3...

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  12. Let A B C D be a parallelogram whose diagonals intersect at P and le...

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  13. Find vec adot vec b when: vec a= hat j- hat k\ a n d\ vec b=2 hat i...

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  14. if vec a=2 hat i- 3 hat j+hat k and vec b=hat i+2 hat j- 3hat k then...

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  15. If vec a=x hat i+y hat j+z hat k , vec b=y hat i+z hat j+x hat k and v...

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  16. Find | -> axx -> b|, if -> a=2 hat i+ hat j+3 hat k and -> b=3 hat i...

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  17. find the value of x,y and z so that the vectors vec a= x hat i+ 2 hat ...

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  18. The lengths of two opposite edges of a tetrahedron are a and b ; the...

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  19. Volume of the parallelopiped whose adjacent edges are vectors veca ...

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  20. Column I, Column II If | vec a+ vec b|=| vec a+2 vec b| , then angel b...

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