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Show that the points A(2hati-hatj+hatk)...

Show that the points `A(2hati-hatj+hatk),B(hati-3hatj-5hatk),C(3hati-4j-4hatk)` are vertices of a right angled triangle.

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Prove that the points hati-hatj,4hati+3hatj+hatk and 2hati-4hatj+5hatk are vertices of a right angled triangle.

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

Show that the vectors hati-hatj-hatk,2hati+3hatj+hatk and 7hati-2hatj-4hatk are coplanar.

Show that the points A, B and C with position vectors, vec(a)=3hati-4hatj-4hatk,vec(b)=2hati-hatj+hatk and vec( c )=hati-3hatj-5hatk , respectively form the vertices of a right angled triangle.

Show that the points A,B and C with position vectors , veca=3hati-4hatj-4hatk,vecb=2hati-hatj+hatkandvecc=hati-3hatj=5hatk ,respectively form the vertices of a right angled triangle.

Show that the vectors hati-3hatj+2hatk,2hati-4hatj-hatk and 3hati+2hatj-hatk and linearly independent.

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

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

The vectors hati+2hatj+3hatk,lamdahati+4hatj+7hatk,-3hati-2hatj-5hatk are collinear, of lamda is equal to

Show that the vectors, vec(a)=hati-2hatj+3hatk,vec(b)=-2hati+3hatj-4hatk and vec( c )=hati-3hatj+5hatk are coplanar.

KUMAR PRAKASHAN-VECTOR ALGEBRA -Textbook Illustrations for Practive Work
  1. Find the vector joining the points P(2,3,0) and Q(-1,-2,-4) directed ...

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  2. Consider two points P and Q with position vectors vec(OP)=3hata-2vec(b...

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  3. Show that the points A(2hati-hatj+hatk),B(hati-3hatj-5hatk),C(3hati-4...

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  4. Find the angle between two vectors vecaandvecb with magnitudes 1 and 2...

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  5. Find angle theta between the vectors veca=hati+hatj-hatkandvecb=hati-h...

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  6. If vec(a)=5hati-hatj-3hatk and vec(b)=hati+3hatj-5hatk, then show that...

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  7. Find the projection of the vector veca=2hati+3hatj+2k on the vector v...

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  8. Find |vec(a)-vec(b)|, if two vectors vec(a) and vec(b) are such that |...

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  9. If vec(a)is a unit vector and (vec(x)-vec(a)).(vec(x)+vec(a))=8 then f...

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  10. For any two vectors vecaandvecb , we always have |veca*vecb|le|veca||v...

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  11. For any two vectors vec(a) and vec(b), we always have |vec(a)+vec(b)|l...

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

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  13. Find |vecaxxvecb|, if veca=2hati+hatj+3hatk and vecb=3hati+5hatj-2hatk

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  14. Find a unit vector perpendicualr to each of the vectors (vec(a)+vec(b)...

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  15. Find the area of atriangle having the points A(1,1,1), B (1,2,3) and C...

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  16. Find the area of a parallelogram whose adjacent sides are given by the...

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  17. If vec(a)=2hati+hatj+3hatk,vec(b)=-hati+2hatj+hatk and vec( c )=3hati+...

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  18. Show that the vectors vec(a)=hati-2hatj+3hatk,vec(b)=-2hati+3hatj-4hat...

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  19. If the vectors vec(a)=hati+3hatj+hatk,vec(b)=2hati-hatj-hatk and vec( ...

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  20. If 4hati+5hatj+hatk,-(hatj+hatk),3hati+9hatj+4hatk and 4(-hati+hatj+ha...

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