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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 ENGLISH-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
  1. Let the pair of vector veca,vecb and vecc,vecd each determine a plane....

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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 3veca-5vecb and 2veca + vecb are mutually perpendicular. If ve...

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  5. the unit vector orthogonal to vector -hati+2hatj+2hatk and making equa...

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  6. The value of x for which the angle between veca=2x^(2)hati+4xhatj + ha...

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  7. If vectors veca and vecb are two adjecent sides of a paralleogram, the...

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  8. A parallelogram is constructed on 3veca+vecb and veca-4vecb, where |ve...

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  9. Let veca.vecb=0 where veca and vecb are unit vectors and the vector ve...

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  10. veca and vecc are unit vectors and |vecb|=4 the angle between veca and...

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

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  12. A vector of magnitude sqrt2 coplanar with the vectors veca=hati+hatj+2...

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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 s...

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  15. Points veca , vecb vecc and vecd are coplanar and (sin alpha)veca + (2...

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  16. If veca and vecb are any two vectors of magnitudes 1and 2. respectivel...

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  17. If veca and vecb are any two vectors of magnitude 2 and 3 respective...

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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 vecu,vecv,vecw be such that |vecu|=1,|vecv|=2,|vecw|3. If the proj...

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