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Let vecf(t)=[t] hat i+(t-[t]) hat j+[t+...

Let ` vecf(t)=[t] hat i+(t-[t]) hat j+[t+1] hat k , w h e r e[dot]` denotes the greatest integer function. Then the vectors ` vecf(5/4)a n df(t),0lttlt1` are(a) parallel to each other(b) perpendicular(c) inclined at `cos^(-1)2 (sqrt(7(1-t^2)))` (d)inclined at `cos^(-1)((8+t)/(9sqrt (1+t^2)))`;

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CENGAGE PUBLICATION-VECTOR ALGEBRA-All Questions
  1. The number of vectors of unit length perpendicular to vectors vec ...

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  2. Prove that ( vec a.hat i)( vec axx hat i)+( vec a.j)( vec axx hat j)+(...

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  3. Let vecf(t)=[t] hat i+(t-[t]) hat j+[t+1] hat k , w h e r e[dot] deno...

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  4. If vec a is parallel to vec bxx vec c , then ( vec axx vec b).( vec ...

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  5. The three vectors hat i+hat j,hat j+hat k, hat k+hat i taken two at a ...

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  6. If vec d= vec axx vec b+ vec bxx vec c+ vec cxx vec a is non-zero vec...

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  7. If |a|=2a n d|b|=3 and adotb=0,t h e n(axx(axx(axx(axxb)))) is equal t...

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  8. If the two diagonals of one its faces are 6 hat i+6 hat ka n d4 hat ...

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  9. The volume of a tetrahedron formed by the coterminous edges vec a ...

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  10. If vec a , vec b , and vec c are three mutually orthogonal unit vector...

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  11. Vector vec c is perpendicular to vectors vec a=(2,-3,1)a n d vec b...

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  12. Given vec a=x hat i+y hat j+2 hat k , vec b= hat i- hat j+ hat k , ve...

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  13. vec aa n d vec b are two unit vectors that are mutually perpendicu...

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  14. If vec ra n d vec s are non-zero constant vectors and the scalar ...

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  15. The scalar vec Adot [( ( vec B+ vec C)xx( vec A+ vec B+ vec C))] eq...

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  16. The volume of he parallelepiped whose sides are given by vec O A=2i...

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  17. For non-zero vectors vec a , vec b ,a n d vec c ,|( vec axx vec b)dot...

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  18. For three vectors vec u , vec va n d vec w which of the following ex...

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  19. Let vec A be a vector parallel to the line of intersection of pla...

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  20. If vec a . vec b=beta and vec axx vec b= vec c ,then vec b is ((beta ...

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