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Write a force of 10 N in x-y plane in ...

Write a force of `10 N ` in x-y plane in terms of unit vectors `hat(i)` and `hat(j)` if it makes an angle `30^(@)` with x-axis as shown in figure :-

A

`5sqrt(3)hat(i)+5hat(j)`

B

`5hat(i)+5sqrt(3)hat(j)`

C

`5hat(i)-5sqrt(3)hat(j)`

D

`5sqrt(3)hat(i)-5hat(j)`

Text Solution

Verified by Experts

The correct Answer is:
A
`10(cos 30^(@))hat(i)+sin 30^(@)hat(j))=(5sqrt(3)hat(i)+ 5hat(j))`
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BANSAL-UNIT DIMENSION, VECTOR & BASIC MATHS-EXERCISE - 1 [SINGLE CORRECT CHOICE TYPE]
  1. If vec(a) be a unit vector, then :-

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  2. If two numerical equal forces P and P acting at a point produce a resu...

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  3. Given that vec(A)+vec(B)=vec(R) and vec(A)+2vec(B) is perpendicular...

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  4. The value of lambda for two perpendicular vectors vec(A)=2vec(i)+lamb...

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  5. The resultant of two vectors of magnitude 3 units 4 units is 1 unit. ...

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  6. If vec(i) and vec(j) are unit vectors along x-axis and y-axis respecti...

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  7. The angle subtended by vector vec(i)+vec(j) with x-axis is :-

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  8. Moment about point whose coordinate is (1,2,3) of a force represented ...

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  9. If vec(A) and vec(B) denote the sides of a parallelogram and its area ...

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  10. A vector perpendicular to (hat(i)+hat(j)+hat(k)) and (hat(i)-hat(j)-...

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  11. The unit vector along vec(i)+vec(j) is :-

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  12. Two constant forces vec(F)(1) and vec(F)(2) acts on a body of mass 8 k...

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  13. Figure shows three vectors a, b and c. If RQ=2PR, which of the followi...

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  14. Component of -10hat(j) in the direction of 3hat(i)-4hat(j) is :-

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  15. If 3hat(i)-2hat(j)+8hat(k) and 2hat(i)+xhat(j)+hat(k) are at right ...

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

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  17. Write a force of 10 N in x-y plane in terms of unit vectors hat(i) a...

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  18. Two vectors vec(A) and vec(B) are such that |vec(A)+vec(B)|=|vec(A)-ve...

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  19. In a clockwise system :-

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  20. vec(a)=3hat(i)+5hat(j),vec(b)=2hat(i)+7hat(j) and vec(c)=hat(i)+9hat(j...

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