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If veca satisfies vecaxx(hati+2hatj+hatk...

If `veca` satisfies `vecaxx(hati+2hatj+hatk)=hati-hatk" then " veca` is equal to

A

`lambdahati+(2lambda-1)hatj+lambdahatk,lambda in R`

B

`lambdahati+(1-2lambda)hatj+lambdahatk,lambda in R`

C

`lambdahati+(2lambda+1)hatj+lambdahatk,lambda in R`

D

`lambdahati+(1+2lambda)hatj+lambdahatk,lambda in R`

Text Solution

Verified by Experts

The correct Answer is:
c
`vecaxx(hati + 2hatj + hatk) = hati-hatk= (hatjxx (hati + 2hatj +hatk))`
`or (veca- hatj) xx (hati + 2hatj +hatk) = vec0`
`or veca - hatj = lambda(hati + 2hatj +hatk)`
`or veca=lambdahati+ (2lambda+1) hatj + lambdahatk , lambda in R`
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CENGAGE PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
  1. Let the pairs a , b,and c ,d each determine a plane. Then the planes a...

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  2. If vecr.veca=vecr.vecb=vecr.vecc=0 " where "veca,vecb and vecc are non...

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  3. If veca satisfies vecaxx(hati+2hatj+hatk)=hati-hatk" then " veca is eq...

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  4. Vectors 3 vec a-5 vec b and 2 vec a+ vec b are mutually perpendicular....

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  5. The unit vector orthogonal to vector -hat i+ hat j+2 hat k and maki...

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  6. The value of x for which the angle between vec a=2x^2 hat i+4x hat ...

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  7. If vectors vec aa n d vec b are two adjacent sides of a parallelogr...

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  8. A parallelogram is constructed on 2 vec a+ vec ba n d vec a-4 vec b...

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  9. Let vec adot vec b=0,w h e r e vec aa n d vec b are unit vectors and ...

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  10. If a \ a n d \ c are unit vectors and |b|=4 . The angel between aa n d...

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  11. Let the position vectors of the points Pa n dQ be 4 hat i+ hat j+lam...

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  12. A vector of magnitude sqrt(2) coplanar with the vector vec a= hat i+ ...

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  13. Let P be a point interior to the acute triangle A B Cdot If P A+P B...

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  14. G is the centroid of triangle ABC and A1 and B1 are the midpoints of...

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  15. Points vec a , vec b , vec c ,a n d vec d are coplanar and (s inalpha...

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  16. If vec aa n d vec b are any two vectors of magnitudes 1 and 2, resp...

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  17. If vec a and vec b are any two vectors of magnitudes 2 and 3, respe...

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  18. veca, vecb and vecc are unit vecrtors such that |veca + vecb+ 3vecc|=4...

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  19. If the vector product of a constant vector vec O A with a variable...

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  20. Let vec u , vec va n d vec w be such that | vec u|=1,| vec v|=2a n d|...

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