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If veca=hati+hatj+hatk, veca.vecb=1 and ...

If `veca=hati+hatj+hatk, veca.vecb=1` and `veca xx vecb = hati-hatk`, then `vecb.(3hati+4hatj+5hatk) =`

A

`hati - hatj + hatk`

B

`2hati - hatk`

C

`hati`

D

`2hati`

Text Solution

Verified by Experts

The correct Answer is:
c
`(veca xx vecb) xxveca = (veca.veca)vecb- (veca.vecb)veca`
`(hatj-hatk)xx (hati +hatj +hatk) = (sqrt3)^(2)vecb - (hati +hatj +hatk)`
`or 3vecb = 3hati or vecb = hati`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -JEE Previous Year (Single Question)
  1. Let vecp,vecq, vecr be three mutually perpendicular vectors of the sam...

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  2. Let veca=2vecj+vecj-2veck,vecb=veci+vecj. If vecc is a vector such tha...

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  3. Let veca = 2i + j+k, vecb = i+ 2j -k and a unit vector vecc be coplana...

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  4. If the vectors veca,vecb,vecc form the sides BC,CA and AB respectively...

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  5. Consider the vectors, vec(a),vec(b),vec(c),vec(d) such that (vec(a)xxv...

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  6. If vec a , vec ba n d vec c are unit coplanar vectors, then the sca...

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  7. If hat a , hat b ,a n d hat c are unit vectors, then | hat a- hat b|^...

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  8. If veca and vecb are two unit vectors such that veca+2vecb and 5veca-4...

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  9. Let vec V=2 hat i+ hat j- hat ka n d vec W= hat i+3 hat kdot If vec ...

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  10. Find the value of a so that the volume of the parallelepiped formed...

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  11. If veca=hati+hatj+hatk, veca.vecb=1 and veca xx vecb = hati-hatk, then...

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  12. The unit vector which is orthogonal to the vector 5hati + 2hatj + 6hat...

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  13. if veca , vecb and vecc are three non-zero, non- coplanar vectors and ...

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  14. Let veca=hati+2hatj +hatk, vec=hati-hatj+hatk and vecc=hati+hatj-hatk....

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  15. Lelt two non collinear unit vectors hata and hatb form and acute angle...

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  16. If veca,vecb,vecc and vecd are unit vectors such that (vecaxxvecb).(ve...

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  17. Two adjacent sides of a parallelogram A B C D are given by vec A B=...

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  18. Let P, Q, R and S be the points on the plane with position vectors -2h...

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  19. Let veca=hati + hatj +hatk,vecb=hati- hatj + hatk and vecc= hati-hatj...

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  20. Let bar(PR)=3hati+hatj-2hatk and bar(SQ)=hati-3hatj-4hatk determine d...

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