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Show that the vector hati+hatj+hatk is e...

Show that the vector `hati+hatj+hatk` is equally inclined with the coordinate axes.

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

Show that the line of intersection of the planes vecr*(hati+2hatj+3hatk)=0 and vecr*(3hati+2hatj+hatk)=0 is equally inclined to hati and hatk . Also find the angleit makes with hatj .

The unit vector which is orthogonal to the vector 5hati + 2hatj + 6hatk and is coplanar with vectors 2hati + hatj + hatk and hati - hatj + hatk is

The unit vector which is orthogonal to the vector 3hati+2hatj+6hatk and is coplanar with the vectors 2hati+hatj+hatk and hati -hatj+hatk is

Show that the vectors hati+2hatj-3hatk , 2hati-hatj+2hatk and 3hati+hatj-hatk are coplanar.

Show that the vectors 3hati-2hatj+hatk,hati-3hatj+5hatk and 2hati+hatj-4hatk form a right angled triangle.

Show that the vectors 2hati-hatj+hatk,hati-3hatj-5hatkand3hati-4hatk form the vertices of a right angled triangle.

Statement 1: Vector vecc = 5hati + 7 hatj + 2hatk is along the bisector of angle between veca = hati + 2hatj + 2hatk and vecb = -8 hati + hatj - 4hatk . Statement 2 : vecc is equally inclined to veca and vecb .

FULL MARKS-VECTOR ALGEBRA-I-ADDITIONAL PROBLEMS
  1. Prove that the points 2hati+3hatj+4hatk,3hati+4hatj+2hatk,4hati+2hatj+...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. Find the vectors of magnitude 6 which are perpendicular to both the ve...

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  16. Find the vectors whose length 5 and which are perpendicular to the vec...

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  17. If vecaxxvecb=veccxxvecd and vecaxxvecc=vecbxxvecd show that veca-vecd...

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  18. Find the angle between two vectors veca nd vecb if abs(vecaxxvecb)=vec...

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  19. If veca,vecb,vecc be unit vectors such that veca.vecb=veca.vecc=0 and ...

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  20. If |veca|=2, |vecb|=7 and vecaxxvecb=3hati-2hatj+6hatk find the angle ...

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