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The two adjacent sides of a parallelogra...

The two adjacent sides of a parallelogram are `2hati-4hatj+5kandhati-2hatj-3hatk`. Find the unit vector parallel to its diagonal Also , find its area.

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The correct Answer is:
`(1)/(7)(3hati-6hatj+2hatk);11sqrt(5)`
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If the diagonals of a parallelogram are 3hati+hatj-2hatk and hati-3hatj+4hatk , then the area of the parallelogram is -

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If the two diagonals of a parallelogram are given by vecR_1=3hati-2hatj+7hatk and vecR_2=5hati+6hatj-3hatk , find out the area of this parallelogram.

If 2hati - 3hatj-hatk & ahati + bhatj- 2hatk these two vectors are parallel to each other. Then find out the value of b.

For given vectors veca=2hati-hatj+2hatkandvecb=-hati+hatj-hatk , find the unit vector in the direction of the vector veca+vecb .

If veca.veci=veca.(hati+hatj)=veca.(hati+hatj+hatk) . Then find the unit vector veca .

If vecA=hati+4hatj+hatk and vecB=3hati-5hatj+hatk , find the unit vector along any vector parallel to the resultant of vecA and vecB .

If vec(AB) = 2 hati- 4 hatj +5 hatk and vec(BC)= hat i-2 hatj-3hatk in parallogram ABCD find a unit vector in direction parallel to the diagonal vec(AC) of the parallelogram.

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NCERT BANGLISH-VECTOR ALGEBRA-Miscellaneous Exercise on chapter 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+5kandhati-2h...

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

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  14. If with reference to the right handed system of mutually perpendicular...

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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*(hatk xx hatj) + hatj*(hati xx hatk)+hatk*(hatj xx h...

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

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