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Find a unit vector in the diection of th...

Find a unit vector in the diection of the vector.
(i) `(3hati + 4hatj - 5hatk)` , (ii) `(3hati - 2hatj + 6hatk)`
(iii) `(hati + hatk)` , (iv) `(2hati + hatj + 2hatk)`

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The correct Answer is:
(i) `((3)/(5sqrt(2))hati + 4/(5sqrt(2))hatj -(5)/(5sqt(2))hatk)` , (ii) `(3/7 hati - 2/7 hatj + 6/7 hatk)`
(iii) `(1/sqrt(2)hati + 1/(sqrt(2))hatk)` , (iv) `(2/3hati + 1/3 hatj + 2/3 hatk)`
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RS AGGARWAL-VECTOR AND THEIR PROPERTIES-Exercise 22
  1. Write down the magnitude of each of the following vectors : (i) vec...

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  2. Find a unit vector in the diection of the vector. (i) (3hati + 4hatj...

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  3. If veca = (2hati - 4hatj + 5hatk) then find the value of lambda so th...

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  4. If veca = (-hati + hatj - hatk) and vecb = (2hati- 2hatj + 2hatk) the...

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  5. If veca = (3hati + hatj - 5hatk) and vecb = (hati + 2hatj - hatk) th...

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  6. If veca = (hati - 2hatj -3hatk) and vecb = (2hati + 4hatj +9 hatk) the...

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  7. Find a vector of magnitude 9 units in the direction of the vector (-2h...

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  8. Find a vector of magnitude 8 units in the direction of the vector (5ha...

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  9. Find a vector of magnitude 21 units in the direction of the vector (2h...

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  10. If veca = (hati - 2hatj), vecb = (2hati - 3hatj) and vecc = (2hati + ...

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  11. If A(-2,1,2) and B(2,-1,6) are two given point, find a unit vector in ...

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  12. Find the direction ratios and direction cosines of the vector veca = (...

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  13. Find the direction ratios and the direction cosines of the vector join...

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  14. Show that the points A,B and C having position vectors (hati + 2hatj +...

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  15. The position vectors of the points A,B and C are (2hati + hatj - hatk)...

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  16. If the position vector of the vertices A,B and C of a DeltaABC be (hat...

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  17. Show that the points A,B and C having position vectors (3hati - 4hatj ...

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  18. Using vector method, show that the points A(1,-1,0), B(4,-3,1) and C(2...

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  19. Find the position vector of the point which divides the join of the po...

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  20. Find the position vector of a point R which divides the line joinin...

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