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Show that the vectors 2hati-hatj+hatk,ha...

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

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

Show that the vectors -hati-2hatj-6hatk,2hati-hatj+hatk" " and -hati+3hatj+5hatk, 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 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 points whose positions vectors 4hati-3hatj+hatk,2hati-4hatj+5hatk,hati-hatj from 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.

Check whether the three vectors 2hati+2hatj+3hatk, vecb=-3hati+3hatj+2hatk and vecc=3hati+4hatk form a triangle or not.

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

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

NCERT TAMIL-VECTOR ALGEBRA-EXERCISE 10.3
  1. Find the angle between two vectors vec a and vec b with magnitudes sqr...

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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 7hati+hatj.

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  4. Find the projection of the vector hat i + 3 hat j + 7 hat k on the vec...

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

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  6. Find |veca|and|vecb|, if (veca+vecb)*(veca-vecb)=8and|veca|=8|vecb|.

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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 |vecx| if for a unit vector veca,(vecx-veca)(vecx+veca)=12

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  10. Given veca=2hati+2hatj+3hatk, vecb=-hati+2hatj+hatk and vecc=3hati+hat...

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  11. Show that |veca|vecb+|vecb|veca is perpendicular to |veca|vecb-|vecb|...

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  12. If vec a. vec a = 0 and vec a. vec b = 0 the what can be concluded abo...

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  13. If veca,vecb,vecc are unit vectors such that veca+vecb+vecc=vec0 , fin...

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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 collinear...

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  17. Show that the vectors 2hati-hatj+hatk,hati-3hatj-5hatkand3hati-4hatk f...

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  18. If veca is a non zero vector of magnitude 'a' and lambda a nonzero sca...

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