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Find a unit vector in the direction of the resultant of the vectors ` hat i- hat j+3 hat k ,""2 hat i+ hat j-2 hat k"and"3 hat i +2 hat j-2 hat k""dot`

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Find the unit vector in the direction of the sum of the vectors 2 hat i+3 hat j- hat k and 4 hat i-3 hat j+2 hat kdot

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Find the direction cosines of the following vectors: 2 hat i+2 hat j- hat k 6 hat i-2 hat j-3 hat k 3 hat i-4 hat k

Find the direction cosines of the following vectors: 2 hat i+2 hat j- hat k 6 hat i-2 hat j-3 hat k 3 hat i-4 hat k

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RD SHARMA ENGLISH-ALGEBRA OF VECTORS-All Questions
  1. If a vector makes angles alpha,beta,gamma. with . OX ,O Ya n dO Z ...

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  2. A B C D is a parallelogram. If L and M are the mid-points of B C and D...

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  3. Find a unit vector in the direction of the resultant of the vectors...

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  4. Find the position vector of the mid-point of the vector joining the...

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  5. Show that the line joining one vertex of a parallelogram to the mid...

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  6. Let vec a , vec b, vec c be three non-zero vectors such that any two ...

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  7. If vec a , vec b are the position vectors of the points (1,-1),(-2,m...

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  8. Find the position vector of a point A in space such that vec O A is i...

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  9. Show that the points A(6,-7,0),B(16 ,-19 ,-4),C(0,3,-6)a n d D(2,-5,1...

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  10. Prove that the lines joining the vertices of a tetrahedron to the ce...

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  11. Find a vector vec r of magnitude 3sqrt(2)u n i t s which makes an an...

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  12. Let vec a= hat i+2 hat ja n d vec b=2 hat i+ hat jdoti s |vec a|=| ve...

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  13. Three vectors of magnitude a ,2a ,3a meet in a point and their directi...

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  14. Show that the vectors vec a-2 vec b+3 vec c , vec a-3 vec b+5 vec ca ...

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  15. Find the angles at which the vector 2 hat i- hat j+2 hat k is inclined...

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  16. Prove that four points 2 vec a+3 vec b- vec c , vec a-2 vec b+3 vec ...

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  17. Find the direction cosines of the vector joining the points A(1,2,-...

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  18. If vec aa n d vec b are two non-collinear vectors, show that points...

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  19. If the position vector vec a of a point (12 ,n) is such that | vec a|...

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  20. If A=(0,1)B=(1,0),C=(1,2),D=(2,1) , prove that vec A B= vec C Ddot

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