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If the position vectors of the points A and B are : `7hat(i)+3hat(j)-hat(k)` and `2hat(i)-5hat(j)+4hat(k)` respectively, find the magnitude and direction - cosines of the vector `vec(AB)`.

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The correct Answer is:
`sqrt(114); lt - (5)/(sqrt(114)), -(8)/(sqrt(114)), (5)/(sqrt(114))gt`.
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MODERN PUBLICATION-VECTOR ALGEBRA -EXERCISE 10 (c ) Short Answer Type Questions
  1. Find the position vector of the mid point of the ne segment A B ,\ wh...

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  2. Find a vector in the direction of the vector 5 hat i - hat j + 2 h...

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  3. Find a vector in the direction of vec a=2 hat i- hat j+2 hat k , whic...

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  4. Find a vector in the direction of : vec(a)=hat(i)-2hat(j)+2hat(k),...

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  5. Find a vector in the direction of : vec(a)=-2hat(i)+hat(j)+2hat(k)...

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  6. Find the scalar components and magnitude of the vector joining the po...

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  7. If |vec(a)|=3, what is : |5vec(a)|

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  8. If |vec(a)|=3, what is : |-2vec(a)|

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  9. If |vec(a)|=3, what is : |0vec(a)| ?

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  10. If vec(a)=3hat(i)-2hat(j)+hat(k), vec(b)=2hat(i)-4 hat(j)-3 hat(k), fi...

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  11. Let vec(a) be a given vector whose initial point is P(x(1), y(1)) and ...

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  12. In the following, find the components of the vector vec(PQ) along x an...

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  13. If the position vectors of the points A and B are : 7hat(i)+3hat(j)-ha...

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  14. Find the position vector of the centroid of the Delta ABC when the pos...

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  15. Show that the vectors vec(a)=2hat(i)+3hat(j) and vec(b)=4hat(i)+6hat(...

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  16. Find a unit vector in the direction of (vec(a)+vec(b)), where : vec(a)...

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  17. If vec(a)=2hat(i)-hat(j)+2hat(k) and vec(b)=6hat(i)+2hat(j)+3hat(k), ...

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  18. Find the unit vector in the direction of vec(a)-vec(b), where : ve...

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  19. If -> a= hat i+ hat j+ hat k , -> b=2 hat i- hat j+3 hat k and -...

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  20. (a) Find the condition that the vectors vec(a)=k hat(i)+l hat(j) and v...

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