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Let veca=2hati-hatj +hatk, vecb=hati+2h...

Let `veca=2hati-hatj +hatk, vecb=hati+2hatj-hatk` and `vecc=hati+hatj-2hatk` be three vectors. A vector of the type `vecb+lambda vecc` for some scalar `lambda`, whose projection on `veca` is of magnitude `sqrt((2)/(3))`, is:

A

`2hati+hatj+5hatk`

B

`2hati+3hatj-3hatk`

C

`-2hati-hatj+5hatk`

D

`2hati+3hatj+3hatk`

Text Solution

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The correct Answer is:
B
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AAKASH SERIES-APPENDICES (REVISION EXERCISE)-DOT PRODUCT OF TWO VECTORS
  1. Let veca and vecb be two unit vectors. If the vectors vecc=hata+2hatb ...

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  2. If hata, hatb & hatc are unit vectors satisfying sqrt(3) veca-vecb=vec...

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  3. Let veca=2hati-hatj +hatk, vecb=hati+2hatj-hatk and vecc=hati+hatj-2h...

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  4. Equation of sphere whose centre is at 7bari-4barj+bark and radius |3b...

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  5. The cartesian equation of the sphere whose centre is C(5, 2, 3) and w...

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  6. The centre and radius of the sphere r^(2) - 2r. (3i + 4j - 5k) + 1 = 0...

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  7. Equation of the sphere described on the join of the points bara=2bari+...

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  8. The radius of the sphere (barr-2bari+3barj-bark). (barr+3bari-barj+2b...

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  9. The cartesian equation of the sphere whose diameter end points are A(1...

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  10. Arrangement of raddi of the following spheres in de-scendin order is ...

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  11. The cartesian equation of the sphere with centre (2, -1, 3) and radi...

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  12. Radius of the sphere r^(2) -2r.(3i+4j-5k)+1=0 is

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  13. Positiion vector of centre of the sphere barr^(2)-barr.(bari+barj+bar...

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  14. The centre and radius of the sphere (bar r-3bari-4barj+5bark)*(barr-2...

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  15. If 2bari and 4bark are the position vectors of the extremities of a di...

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  16. If the position vector of one end A of a diameter AB of the sphere |ba...

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  17. For a sphere, ends of a diameter have position vectors bara and -bara,...

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  18. If |barc|^(2)=60 and barc xx (bari+2barj+5bark)=bar0 then a value of b...

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  19. If barx, bary, barz are three unnit vectors in three - dimensional spa...

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  20. |bara|=2, |barb|=3 and |2bara-barb|=5 then |2bara+barb| equals:

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