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Let a=2i−j+k , b=i+2j−k and c=i+j−2k be...

Let `a=2i−j+k` , `b=i+2j−k` and `c=i+j−2k` be three vectors. A vector r in the plane of b and c whose projection on a is of magnitude `sqrt(2/3)` ​ ​ is

A

`2hati+3hatj-3hatk`

B

`-2hati-hatj+5hatk`

C

`2hati+3hatj+3hatk`

D

`2hati+hatj+5hatk`

Text Solution

Verified by Experts

The correct Answer is:
b
Let the required vector be `vecr`. Then
`vecr = x_(1) vecb + x_(2) vecc and vecr .veca = sqrt(2/3) " " (|veca|)=2`
Now ` vecr.veca = x_(1) veca. Vecb + x_(2) veca.vecc`
` Rightarrow 2 = x_(1) ( 2-2-1) + x_(2) ( 2-1-2)`
` Rightarrow x_(1) + x_(2) = -2`
` Rightarrow vecr = x_(1) ( hati + 2hatj -hatk) + x_(2) (hati +hatj - 2hatk)`
`= hati (x_(1) + x_(2) +hatj ( 2x_(1) + x_(2) ) -hatk ( 2x_(2) +x_(1))`
` 2hati + hatj (x_(1) -2) -hatk(-4-x_(1))`,
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CENGAGE PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
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  6. veca and vecb are two unit vectors that are mutually perpendicular. A...

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  7. Given that vec a , vec b , vec p , vec q are four vectors such that ...

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  8. The position vectors of the vertices A ,Ba n dC of a triangle are th...

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  9. If a is real constant A ,B and C are variable angles and sqrt(a^2-4)ta...

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  10. The vertex A triangle A B C is on the line vec r= hat i+ hat j+lambda...

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  11. A non-zero vector vec a is such that its projections along vectors ...

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

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  13. In a quadrilateral A B C D , vec A C is the bisector of vec A Ba n d ...

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  14. In fig. A B ,D Ea n dG F are parallel to each other and A D ,B Ga n...

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  15. Vector vec a in the plane of vec b=2 hat i+ hat ja n d vec c= hat i-...

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

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

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

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