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The scalar product of the vector hati+ha...

The scalar product of the vector `hati+hatj+hatk` with a unit vector along the sum of vectors `2hati+4hatj-5hatk` and `lambda hati+2hatj+3hatk` is equal to one. Find the value of `lambda`.

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The correct Answer is:
`lambda=1`
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KUMAR PRAKASHAN-VECTOR ALGEBRA -MISCELLANEOUS EXERCISE - 10
  1. Write down a unit vector in XY-plane, making an angle of 30^(@) with t...

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  2. Find the scalar components and magnitude of the vector joining the poi...

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  3. A girl walks 4 km towards west, then she walks 3 km in a direction 30^...

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  4. If veca=vecb+vecc , then is it true that |veca|=|vecb|+|vecc|? Justify...

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  5. Find the value of x for which x(hati+hatj+hatk) is a unit vector.

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  6. Find a vector of magnitude 5 units and parallel to the resultant of th...

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  7. If veca=hati+hatj+hatk,vecb=2hatj-hatj+3hatkandvecc=hati-2hatj+hatk, ...

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  8. Show that the points A(1,-2,-8),B(5,0,-2)andC(11,3,7) are collinear , ...

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  9. Find the position vector of a point R which divides the line joining t...

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  10. The two adjacent sides of a parallelogram are 2hati-4hatj+5hatk and ha...

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  11. Show that the direction cosines of a vector equally inclined to the ax...

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  12. Let vec(a)=hati+4hatj+2hatk,vec(b)=3hati-2hatj+7hatk and vec( c )=2hat...

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  13. The scalar product of the vector hati+hatj+hatk with a unit vector alo...

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  14. If vec(a),vec(b),vec( c ) are mutually perpendicular vectors of equal ...

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  15. prove that (vec(a)+vec(b)).(vec(a)+vec(b))=|vec(a)|^(2)+|vec(b)|^(2), ...

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  16. If theta is angle between two vectors vec(a) and vec(b) then vec(a).ve...

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  17. Let vec(a) and vec(b) be two unit vectors and theta is the angle betwe...

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  18. The value of hati.(hatj xx hatk)+hatj.(hati xx hatk)+hatk.(hati xx hat...

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  19. If theta is the angle between any two vectors vecaandvecb, then |veca*...

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