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For any vector vecr prove that vecr=(vec...

For any vector `vecr` prove that `vecr=(vecr.hati)hati+(vecr.hatj)hatj+(vecr.hatk)hatk`.

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For any vector prove that vecr=(vecr.veci)i+(vecr.vecj)j+(vecr.veck)k

Convert the vector vecr=3hati+2hatj into a unit vector.

Find the distance between the parallel planes vecr*(-hati-hatj+hatk)=3, vecr*(hati+hatj-hatk)=5 .

Determine whether the lines vecr=(hati-hatj)+t(hati-hatj+3hatk) and vecr=(2hati+hatj-hatk)+s(hati+2hatj-hatk) are parallel. Find the shortest distance between them.

Find the distance between the parallel lines vecr=(hati-hatj)+t(2hati-hatj+hatk) and vecr=(2hati+hatj-hatk)+s(2hati-hatj+hatk) .

A unit vector parallel to the intersection of the planes vecr.(hati-hatj+hatk)=5 andvecr.(2hati+hatj-3hatk)=4 is

Find the equation of the plane passing through the line of intersection of the planes vecr.(hati+hatj+hatk)=1 and vecr.(2hati+3hatj-hatk)+4=0 and parallel to x axis.

Find the vector equation of the plane passing through the intesection of the planes vecr.(2hati+2hatj-3hatk)=7, vecr.(2hati+5hatj+3hatk)=9 and through the point (2,1,3).

The centre of the circle given by vecr.(hati+2hatj+2hatk)=15and|vecr-(hatj+2hatk)=4 is

FULL MARKS-VECTOR ALGEBRA-I-ADDITIONAL PROBLEMS
  1. For any vector vecr prove that vecr=(vecr.hati)hati+(vecr.hatj)hatj+(v...

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  2. Shown that the points with position vectors veca-2vecb+3vecc,-2veca+3v...

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  3. If ABC and A'B'C' are two triangles and G, Gʻ be their corresponding c...

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  4. Prove using vectors the mid-points of two opposite sides of a quadrila...

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  5. Show that the vectors 2hati-3hatj+4hatk are -4hati+6hatj-8hatk are col...

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  6. Find the unit vectors parallel to the sum of 3hati-5hatj+8hatk and -2h...

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  7. Show that the points whose position vectors are 4veci +5vecj+6veck, 5v...

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  8. Prove that the points 2hati+3hatj+4hatk,3hati+4hatj+2hatk,4hati+2hatj+...

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  9. Examine whether the vectors hati+3hatj+hatk,2hati-hatj-hatk and 7hatj+...

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  10. Find lamda so that the vectors 2hati+lamdahatj+hatk and hati-2hatj+hat...

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  11. If |veca+vecb|=60,|veca-vecb|=40" ""and"" " |vecb|=46,"then" |veca|is

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  12. If the sum of two unit vectors is a unit vector prove that the magnitu...

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  13. Show that the vectors 3hati-2hatj+hatk,hati-3hatj+5hatk and 2hati+hatj...

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  14. Find the projection of : (i) hati-hatj on Z-axis (ii) hati+2hatj-2ha...

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  15. Show that the vector hati+hatj+hatk is equally inclined with the coord...

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  16. If veca,vecb,vecc are three mutually perpendicular unit vectors, then ...

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  17. Show that the points whose positions vectors 4hati-3hatj+hatk,2hati-4h...

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  18. Let vec(u),vec(v),vec(w)" be vectors such that "vec(u)+vec(v)+vec(w)=v...

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  19. If vecp=-3veci+4vecj-7veck ans vecq=6veci+2vecj-3veck then find vecpxx...

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  20. If veca.vecb are say two vectors, then prove that abs(vecaxxvecb)^(2)+...

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  21. Find the angle between the vectors 2hati+hatj-hatk and hati+2hatj+hatk...

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