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

Prove that the points `2hati+3hatj+4hatk,3hati+4hatj+2hatk,4hati+2hatj+3hatk` from an equilateral triangle.

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Prove that points hati+2hatj-3hatk, 2hati-hatj+hatk and 2hati+5hatj-hatk form a triangle in space.

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

Show that the points whose positions vectors 4hati-3hatj+hatk,2hati-4hatj+5hatk,hati-hatj from a right angled triangle.

Show that the vectors -hati-2hatj-6hatk,2hati-hatj+hatk" " and -hati+3hatj+5hatk, form a right angled triangle.

Prove that the points whose position vectors 2hati+4hatj+3hatk,4hati+hatj+9hatk and 10hati-hatj+6hatk form a right angled triangle.

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

Show that the points vectors are 2hati+3hatj-5hatk,3hati+hatj-2hatk and 6hati-5hatj+7hatk are collinear.

If 2hati-hatj+3hatk,3hati+2hatj+hatk,hati+mhatj+4hatk are coplanar, find the value of m.

Show that the points A(-2hati+3hatj+5hatk),B(hati+2hatj+3hatk)andC(7hati-hatk) are collinear.

FULL MARKS-VECTOR ALGEBRA-I-ADDITIONAL PROBLEMS
  1. Find the unit vectors parallel to the sum of 3hati-5hatj+8hatk and -2h...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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