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A non-zero vector vec a is such that it...

A non-zero vector ` vec a` is such that its projections along vectors `( hat i+ hat j)/(sqrt(2)),(- hat i+ hat j)/(sqrt(2))` and ` hat k` are equal, then unit vector along ` vec a` is a.`(sqrt(2) hat j- hat k)/(sqrt(3))` b. `( hat j-sqrt(2) hat k)/(sqrt(3))` c. `(sqrt(2))/(sqrt(3)) hat j+( hat k)/(sqrt(3))` d. `( hat j- hat k)/(sqrt(2))`

A

`(sqrt2hatj-hatk)/sqrt3`

B

`(hatj-sqrt2hatk)/sqrt3`

C

`sqrt2/sqrt3hatj+hatk/sqrt3`

D

`(hatj - hatk)/(sqrt2)`

Text Solution

Verified by Experts

The correct Answer is:
a
Let the projection be x then ,
`veca= (x(hati +hatj))/sqrt2+(x(-hati+hatj))/sqrt2+xhatk`
`veca= (2xhatj)/sqrt2+ xhatk or hata= sqrt2/sqrt3hatj + hatk/sqrt3`
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CENGAGE PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
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  7. Vector vec a in the plane of vec b=2 hat i+ hat ja n d vec c= hat i-...

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  8. Let A B C D be a tetrahedron such that the edges A B ,A C and A D ar...

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  9. 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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  13. If |veca|=2 and |vecb|=3 and veca.vecb=0, " then "| (vecaxx(vecaxx(vec...

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

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

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

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