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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.

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

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

Find [vec(a)vec(b)vec( c )] if vec(a)=hati-2hatj+3hatk,vec(b)=2hati-3hatj+hatk and vec( c )=3hati+hatj-2hatk .

If the vectors vec(a)=hati+3hatj+hatk,vec(b)=2hati-hatj-hatk and vec( c )=lambda hati+7hatj+3hatk are coplannar then find lambda .

vec(a)=hati-2hatj+hatk,vec(b)=2hati+hatj+hatk , vec( c )=hati+2hatj-hatk then find that vec(a)xx(vec(b)xxvec( c )) .

Consider points A,B,C annd D with position vectors 7hati-4hatj+7hatk,hati-6hatj+10hatk,-1hati-3hatj+4hatk and 5hati-hatj+5hatk , respectively. Then, ABCD is

vec(a)=2hati-10hatj+2hatk,vec(b)=3hati+hatj+2hatk and vec( c )=2hati+hatj+3hatk then find vec(a)xx(vec(b)xxvec( c )) .

If a=3hati-2hatj+hatk,b=2hati-4hatj-3hatk and c=-hati+2hatj+2hatk , then a+b+c is

KUMAR PRAKASHAN-VECTOR ALGEBRA -EXERCISE-10.2
  1. Compute the magnitude of the following vectors : veca=hati+hatj+k,...

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  2. Compute the magnitude of the following vectors : veca=hati+hatj+k,...

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  3. Write two different vectors having same magnitude.

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  4. Write two different vectors having same direction.

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  5. Find the values of x and y so that the vectors 2hati+3hatjandxhati+yh...

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  6. Find the scalar and vector components of the vector with initial poi...

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  7. Find the sum of the vectors veca=hati-2hatj+hatk,vecb=-2hati+4hatj+5h...

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  8. Find the unit vector in the direction of the vector veca=hati+hatj+2h...

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  9. Find the unit vector in the direction of vector vec(PQ) , where P and ...

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  10. For given vectors veca=2hati-hatj+2hatkandvecb=-hati+hatj-hatk, find t...

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  11. Find a vector in the direction of vector 5hati-hatj+2hatk which has ma...

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

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  13. Find the direction cosines of the vector hati+2hatj+3hatk.

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  14. Find the direction cosines of the vector joining the points A(1,2,-3)...

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  15. Show that the vector hati+hatj+hatk is equally inclined to the axes OX...

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

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  17. Find the position vector of the mid point of the vector joining the p...

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  18. Show that the points A, B and C with position vectors, vec(a)=3hati-4h...

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  19. If triangle ABC (Fig 10.18), which of the following is not true : (A...

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  20. If vec(a) and vec(b), are two collinear vectors, then which of the fol...

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