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The two adjacent sides of a parallelogra...

The two adjacent sides of a parallelogram are given by the vectors `2hati-4hatj+5hatk` and `hati-2hatj-3hatk` Find a unit vector parallel to its diagonal (longer). Also find the area of parallelogram.

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MODERN PUBLICATION-VECTORS-Exercise
  1. If veca=2hati-hatj+hatk,vecb=hati+3hatj-hatk,vecc=-2hati+hatj-3hatk an...

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

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  3. The two adjacent sides of a parallelogram are given by the vectors 2ha...

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

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  5. If veca, vecb, vecc are mutually perpendicular vectors of equal magnit...

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  6. If veca,vecb,vecc are three non-coplanar vectors and vecd*veca=vecd*ve...

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  7. If vecc is normal to veca and vecb, show that vecc is normal to veca+v...

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  8. Show that |veca|vecb + |vecb|veca is perpendicular to |veca|vecb-|vec...

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  9. Find the area of the parallelogram having diagonals veca+vecb and vecb...

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  10. Prove that the quadrilateral obtained by joining mid-points of adjacen...

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  11. Prove that 1/2 vec(AC)xxvec(BD) represents the vector area of the plan...

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  12. Given veca=1/7(2hati+3hatj+6hatk), vecb=1/7(3hati-6hatj+2hatk) , ve...

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  13. If veca,vecb,vecc are coplanar then show that veca+vecb, vecb+vecc and...

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  14. Are vectors veca and -veca collinear ?

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  15. Write two different vectors having same magnitude.

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  16. What is the unit vector in the direction of veca=veci+vecj+2veck?

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  17. What is the position vector of the mid-point of the line segment joini...

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  18. The scalar product of two given vectors veca and vecb having angle 'th...

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  19. For mutually perpendicularl unit vectors hati,hatj,hatk, we have : hat...

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  20. What is the value of : hati*(hatjxxhatk)+hatj.(hatkxxhati)+hatk.(hatjx...

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