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The unit vector in the opposite directio...

The unit vector in the opposite direction of `bar(x)+bar(y)-2bar(z)` is ………… where `bar(x)=(1,1,0),bar(y)=(0,1,1)` and `bar(z)=(1,0,1)`.

A

`((1)/(sqrt(6)),(-2)/(sqrt(6)),(1)/(sqrt(6)))`

B

`((1)/(6),(-2)/(6),(1)/(6))`

C

`((-1)/(sqrt(6)),(2)/(sqrt(6)),(-1)/(sqrt(6)))`

D

`((-1)/(6),(2)/(6),(-1)/(6))`

Text Solution

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The correct Answer is:
A
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KUMAR PRAKASHAN-VECTOR ALGEBRA -Solutions of NCERT Exemplar Problems (Multiple Choice Questions (MCQs) )
  1. The unit vector parallel to the vecotr bar(a)-bar(b) is ……………. where...

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  2. If bar(a)=(1,1,1),bar(b)=(4,-2,3) and bar( c )=(1,-2,1) then the vect...

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  3. The unit vector in the opposite direction of bar(x)+bar(y)-2bar(z) is ...

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  4. The vector with magnitude 17sqrt(2) and in the opposite direction of (...

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  5. Out of the following …………. Is the unit vector in the direction of (3ha...

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  6. The position vector of the point P is (4, 5, -3). The distance of the ...

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  7. The position vector of a point A is (4, 2, -3). If the distance of the...

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  8. vec(a)=hati+hatj+hatk,vec(b)=hati-hatj+hatk and vec( c )=hati+2hatj-...

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  9. A(1, 1, 2), B(4, 3, 1) and C(2, 3, 5) are vertices of a triangle ABC. ...

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  10. The position vectors of two points A and B are respectively 6vec(a)+2v...

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  11. The position vectors of the vertices of triangle are 3hati+4hatj+5hatk...

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  12. The angle between the unit vectors vec(a) and vec(b) is 2theta. Where ...

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  13. squareABCD is a parallelogram. (A(1)) and B(1) are midpoints of the si...

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  14. In DeltaABC,vec(AB)=3hati+4hatk and vec(AC)=5hati-2hatj+4hatk. Length ...

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  15. If bar(x)=(a,4,2a) and bar(y)=(2a,-1,a) are perpendicualr to each othe...

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  16. If bar(x)=(3,1,0),bar(y)=(2,2,3),bar(z)=(-1,2,1). If bar(x)|(bar(y)+...

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  17. If bar(x)=(1,2,4),bar(y)=(-1,-2,k),k ne -4 then |bar(x).bar(y)|………|bar...

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  18. If bar(a)=(-3,1,0) and bar(b)=(1,-1,-1) then "Comp"(bar(a))bar(b) …………...

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  19. The projection of (1, 2, -1) on hati is …………….

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  20. A(3,-1),B(2,3) and C(5,1) are given then m angleA = ………

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