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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.

NCERT GUJARATI-VECTOR ALGEBRA-Miscellaneous Exercise on chapter 10
  1. Show that the points A(2hati-hatj+hatk),B(hati-3hatj-5hatk),C(3hati-4...

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  2. Write down a unit vector in XY-plane, making an angle of 30^(@) with t...

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  3. Find the scalar components and magnitude of the vector joining the poi...

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  4. A girl walks 4 km towards west, then she walks 3 km in a direction 30^...

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  5. If veca=vecb+vecc , then is it true that |veca|=|vecb|+|vecc|? Justify...

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  6. Find the value of x for which x(hati+hatj+hatk) is a unit vector.

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  7. A vector has magnitude 5 units. It is parallel to the resultant vector...

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

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  9. Show that the points A(1,-2,-8),B(5,0,-2)andC(11,3,7) are collinear , ...

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  10. Find the position vector of a point R which divides the line joining t...

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  11. The two adjacent sides of a parallelogram are 2hati-4hatj+5kandhati-2h...

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  12. Show that the direction cosines of a vector equally inclined to the ax...

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  13. Let veca=hati+4hatj+2hatk,vecb=3hati-2hatj+7hatkandvecc=2hati-hatj+4ha...

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  14. The scalar product of the vector hati+hatj+hatk with a unit vector alo...

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  15. Prove that (veca+vecb)*(veca+vecb)=|veca|^(2)+|vecb|^(2), if and only...

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  16. If theta is angle between two vectors vec(a) and vec(b) then vec(a).ve...

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  17. Let vec(a) and vec(b) be two unit vectors and theta is the angle betwe...

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  18. The value of hati.(hatjxxhatk)+hatj*(hatixxhatk)+hatk*(hatixxhatj) is

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  19. If theta is the angle between any two vectors vecaandvecb, then |veca*...

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