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Find the value of x for which x (hat i +...

Find the value of x for which `x (hat i + hat j + hat k)` is a unit vector.

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The correct Answer is:
`+-(1)/(sqrt(3))`
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Thescalar product of the vector hat i + hat j + hat k with a unit vector along the sum of vectors 2 hat i + 4 hat j - 5 hat k and lambda hat i + 2 hat j + 3 hat k is equal to one. Find the value of lambda .

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NCERT TAMIL-VECTOR ALGEBRA-Miscellaneous Exercise on chapter 10
  1. Write down a unit vector in XY - plane making an angle of 30^(@) with ...

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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 = vec b+ vec c, then is it true that |veca| = |vec b| + |vec ...

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  5. Find the value of x for which x (hat i + hat j + hat k) is a unit vect...

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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=2hati-hatj+3hatkandvecc=hati-2hatj+hatk, ...

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

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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 2 hat i - 4 hat j + 5 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 veca=hati+4hatj+2hatk,vecb=3hati-2hatj+7hatkandvecc=2hati-hatj+4ha...

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  13. Thescalar product of the vector hat i + hat j + hat k with a unit vect...

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  14. If veca,vecb,vecc are mutually perpendicular vectors of equal magnitu...

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  15. Prove that (veca+vecb)*(veca+vecb)=|veca|^(2)+|vecb|^(2), if and only...

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  16. If theta is the angle between two vectors vecaandvecb then veca*vecbge...

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  17. Let vecaandvecb be two unit vectors and theta is the angle between the...

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  18. The value of hati.(hatjxxhatk)+hatj.(hatkxxhati)+hatk.(hatjxxhati) ...

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  19. If theta is the angle between any two vectors vec a and vec b , then |...

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