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If bar(a)=hati+hatj+2hatk and bar(b)=2ha...

If `bar(a)=hati+hatj+2hatk` and `bar(b)=2hati+hatj-2hatk`, find the unit vector in the direction of
(i) `6bar(b)" "` (ii) `2bar(a)-bar(b)`

Text Solution

Verified by Experts

The correct Answer is:
`=(2)/(3)hati+(1)/(2)hatj-(2)/(3)hatk`
`=0i+(1)/(sqrt(37))j+(6)/(sqrt(37))k`
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KUMAR PRAKASHAN-VECTOR ALGEBRA -Solutions of NCERT Exemplar Problems (Short Answer Type Questions)
  1. Find the unit vector in the direction of sum of vectors vec(a)=2hati-h...

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  2. If bar(a)=hati+hatj+2hatk and bar(b)=2hati+hatj-2hatk, find the unit v...

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  3. Find a unit vector in the direction of vec(PQ), where P and Q have coo...

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  4. If A and B are the positon vectors of bar(a) and bar(b) respectively, ...

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  5. Using vectors, find the value of k, such that the points (k,-10,3),(1,...

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  6. A vector bar( r ) is inclined at equal angles to the three axes. If th...

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  7. If a vector vec( r ) has magnitude 14 and direction ratios 2, 3, -6. T...

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  8. Find a vector of magnitude 6, which is perpendicualr to both the vecto...

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  9. Find the angle between the vectors 2hati-hatj+hatk and 3hati+4hatj-hat...

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  10. If bar(a)+bar(b)+bar( c )=0, then show that bar(a)xx bar(b)=bar(b)xx b...

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  11. Find the sine of the angle between the vectors bar(a)=3hati+hatj+2hatk...

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  12. If A, B, C and D are the points with position vectors hati+hatj-hatk,2...

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  13. Using vectors, find the area of the DeltaABC with vertices A(1,2,3),B(...

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  14. Using vectors, prove that the parallelogram on the same base and betwe...

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  15. Prove that in any DeltaABC,cos A=(b^(2)+c^(2)-a^(2))/(2bc) where a, ...

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  16. Show that area of the parallelogram whose diagonals are given by vec(a...

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  17. If bar(a)=bar(i)+bar(j)+bar(k) and bar(b)=bar(j)-bar(k), then find a v...

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