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Shown that the points with position vect...

Shown that the points with position vectors `veca-2vecb+3vecc,-2veca+3vecb+2vecc` and `-8veca+13vecb` are collinear.

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The vectors veca-vecb,vecb-vecc,vecc-veca are

If veca, vecb and vecc are non-coplanar vectors, prove that the four points 2veca+3vecb-vecc, veca-2vecb+3vecc, 3veca+4vecb-2vecc and veca-6vecb+ 6 vecc are coplanar.

Show that the vectors 2veca-vecb+3vecc, veca+vecb-2vecc and veca+vecb-3vecc are non-coplanar vectors (where veca, vecb, vecc are non-coplanar vectors).

[veca, veca+vecb, veca+vecb+vecc] is :

Let veca,vecb and vecc be non-coplanar vectors. Let A,B and C be the points whose position vectors with respect to the origin O are veca+2vecb+3vecc,-2veca+3vecb+5vecc and 7veca-vecc respectively. Then prove that A, B and C are collinear.

If veca, vecb and vecc are three non-zero, non-coplanar vectors,then find the linear relation between the following four vectors : veca-2vecb+3vecc, 2veca-3vecb+4vecc, 3veca-4vecb+ 5vecc, 7veca-11vecb+15vecc .

Prove that [veca+vecb vecb+vecc vecc+veca]=2[veca vecb vecc]

A, B C and D are four points in a plane with position vectors, veca, vecb vecc and vecd respectively, such that (veca-vecd).(vecb-vecc)= (vecb-vecd).(vecc-veca)=0 then point D is the ______ of triangle ABC.

The vectors veca and vecb are non collinear. Find for what value of x the vectors vecc=(x-2)veca+vecb and vecd=(2x+1) veca-vecb are collinear.?

FULL MARKS-VECTOR ALGEBRA-I-ADDITIONAL PROBLEMS
  1. Shown that the points with position vectors veca-2vecb+3vecc,-2veca+3v...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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