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Find a unit vector parallel to the sum o...

Find a unit vector parallel to the sum of the vector `(hati + hatj + hatk)` and `(2hati - 3hatj + 5hatk)`.

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The correct Answer is:
Let `veca = (hati hatj + hatk)` and `vecb = (2hati - 3hatk + 5hatk)`. Then,
`(veca+vecb) = (hati + hatj + hatk) + (2hati - 3hatj + 5hatk) = (3hati - 2hatj + 6hatk)`
Required unit vectors parallel to `(veca + vecb)` are
`+-((3hati - 2hatj + 6hatk))/(sqrt(3^(2) + (-2)^(2) + 6^(2))) = +- 1/7(3hati - 2hatj + 6hatk)`.

Let `veca = (hati hatj + hatk)` and `vecb = (2hati - 3hatk + 5hatk)`. Then,
`(veca+vecb) = (hati + hatj + hatk) + (2hati - 3hatj + 5hatk) = (3hati - 2hatj + 6hatk)`
Required unit vectors parallel to `(veca + vecb)` are
`+-((3hati - 2hatj + 6hatk))/(sqrt(3^(2) + (-2)^(2) + 6^(2))) = +- 1/7(3hati - 2hatj + 6hatk)`.
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RS AGGARWAL-VECTOR AND THEIR PROPERTIES-Exercise 22
  1. Find a unit vector parallel to the sum of the vector (hati + hatj + ha...

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  2. Write down the magnitude of each of the following vectors : (i) vec...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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