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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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Hence, `DeltaABC` is 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 -EXERCISE-10.3
  1. Find the angle between two vectors vecaandvecb with magnitudes sqrt(3)...

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  2. Find the angle between the vectors hati-2hatj+3hatkand3hati-2hatj+hatk

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  3. Find the projection of the vector hati-hatj on the vector hati+hatj.

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  4. Find the projection of the vector hati+3hatj+7hatk on the vector 7hati...

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  5. Show that each of the given three vectors is a unit vector. (1)/(7)(2h...

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  6. Find |vec(a)| and |vec(b)|, if (vec(a)+vec(b)).(vec(a)-vec(b))=8 and |...

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  7. Evaluate the product (3veca-5vecb)*(2veca+7vecb).

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  8. Find the magnitude of two vectors vecaandvecb , having the same magni...

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  9. Find |vec(x)|, iif for a unit vector vec(a), (vec(x)-vec(a)).(vec(x)...

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  10. If veca=2hati+2hatj+3hatk,vecb=-hati+2hatj+hatkandvecc=3hati+hatj are...

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  11. Show that |vec(a)|vec(b)+|vec(b)|vec(a) is perpendicualr to |vec(a)|ve...

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  12. If vec(a).vec(a)=0 and vec(a).vec(b)=0 then what can be concluded abou...

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  13. If vec(a),vec(b),vec( c ) are unit vectors such that vec(a)+vec(b)vec(...

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  14. If either vector veca=vec0orvecb=vec0, , then veca*vecb=0. But the c...

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  15. If either vector A,B,C of a triangle ABC are (1,2,3),(-1,0,0),(0,1,2)...

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  16. Show that the points A(1, 2, 7), B(2, 6, 3) and C(3, 10, -1) are colli...

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

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  18. If veca is a nonzero vector of mangitude 'a' and lambda a nonzero scal...

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