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Position vector hat k is rotated about ...

Position vector ` hat k` is rotated about the origin by angle `135^0` in such a way that the plane made by it bisects the angel between ` hat ia n d hatjdot` Then its new position is `+-( hat i)/(sqrt(2))+-( hat j)/(sqrt(2))` b. `+-( hat i)/2+-( hat j)/2-( hat k)/(sqrt(2))` c. `( hat i)/(sqrt(2))-( hat k)/(sqrt(2))` d. none of these

A

`+-hati/sqrt2+-hatj/sqrt2`

B

`+-hati/2+-hatj/2-hatk/sqrt2`

C

`hati/sqrt2-hatk/sqrt2`

D

none of these

Text Solution

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The correct Answer is:
d
Let `vecr` be the new position . Then `vecr= lambdahatk + mu ( hati + hatj) `
` Also, vecr.hatk = - 1/sqrt2 Rightarrow lambda= - 1/sqrt2`
` Also lambda^(2)+ 2mu^(2) = 1 Rightarrow 2mu^92) = 1/2 or mu = +- 1/2`
` vecr = +- 1/2 (hati + hatj) =- hatk/sqrt2`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
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  2. A non-zero vecto veca is such tha its projections along vectors (hati ...

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  3. Position vector hat k is rotated about the origin by angle 135^0 i...

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  4. ln a quadrilateral ABCD, vec(AC) is the bisector of the (vec(AB) ^^ v...

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  5. In fig. 2.33 AB, DE and GF are parallel to each other and AD, BG and E...

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  6. Vectors hata in the plane of vecb = 2 hati +hatj and vecc = hati-hatj ...

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

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  8. 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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  9. If veca is parallel to vecb xx vecc, then (veca xx vecb) .(veca xx vec...

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

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  11. If vecd=vecaxxvecb+vecbxxvecc+veccxxveca is a on zero vector and |(vec...

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

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

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

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

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

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

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

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

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