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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),0

A

parallel to each other

B

perpendicular to each other

C

inclined at `cos^(-1) 2/(sqrt7(1-t^(2))`

D

inclined at `cos ^(-1) (8+t)/(9sqrt(1+t^(2)))`

Text Solution

Verified by Experts

The correct Answer is:
d
`vecf""(5/4)= [5/4] hati+ (5/4-[5/4])hatj + [5/4=1]hatk`
`hati+ (5/4-1)hatj + 2hatk`
`hati + 1/4 hatj + 2hatk`
when `0 lt t 1 ,vecf "" (t) = 0 hati + { t-0} hatj +hatk`
` hatj +hatk`
` vecf "" (5/4) .vecf"" (t) = 2+t/4`
so, `costheta= 4/(|vect+1/4hatj + 2hatk||thatj +hatk|)`
`(2+t/4)/(sqrt(1+1/16=4)sqrt(1+t^(2)))`
` ( 8 +t)/(9sqrt(1 + t^(2)))`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. Vectors hata in the plane of vecb = 2 hati +hatj and vecc = hati-hatj ...

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  2. Let A B C D be a tetrahedron such that the edges A B ,A Ca n dA D a...

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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 veca is parallel to vecb xx vecc, then (veca xx vecb) .(veca xx 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 vecd=vecaxxvecb+vecbxxvecc+veccxxveca is a on zero vector and |(vec...

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  7. If |veca|=2 and |vecb|=3 and veca.vecb=0, " then " (vecaxx(vecaxx(veca...

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  8. If two diagonals of one of its faces are 6hati + 6 hatk and 4 hatj + ...

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  9. The volume of a tetrahedron fomed by the coterminus edges veca , vecb ...

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  10. If veca ,vecb and vecc are three mutually orthogonal unit vectors , th...

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  11. vector vecc are perpendicular to vectors veca= (2,-3,1) and vecb= (1,...

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  12. Given veca=xhati+yhatj+2hatk,vecb=hati-hatj+hatk , vecc=hati+2hatj, ve...

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  13. Let veca=a(1)hati+a(2)hatj+a(3)hatk, vecb=b(1)hati+b(2)hatj+b(3)hatk a...

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  14. Let vecr, veca, vecb and vecc be four non-zero vectors such that vecr....

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  15. If veca, vecb and vecc are such that [veca vecb vecc] =1, vecc= lambda...

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  16. If 4veca+5vecb+9vecc=0 " then " (vecaxxvecb)xx[(vecbxxvecc)xx(veccxxve...

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  17. Value of [vec a xx vec b,vec a xx vecc,vec d] is always equal to

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  18. Let hata and hatb be mutually perpendicular unit vectors. Then for an...

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  19. Let veca and vecb be unit vectors that are perpendicular to each other...

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  20. veca and vecb are two vectors such that |veca|=1 ,|vecb|=4 and veca. V...

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