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Which of the followingis a unit vector ?...

Which of the followingis a unit vector ?

A

`hat(i)+hat(j)`

B

`costhetahat(i)-sinthetahat(j)`

C

`sinthetahat(i)+2costhetahat(j)`

D

`(1)/(sqrt(3))(hat(i)+hat(j))`

Text Solution

Verified by Experts

The correct Answer is:
B
(b) Unit vector has a magnitude equal to 1
Here, `sqrt(cos^(2)theta+sin^(2)theta)=1`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-SCALARS AND VECTORS -Exercise 2 (Miscellaneous Problems)
  1. A vetor is added to an equal and oppsite vector of similar nature,form...

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  2. Which of the followingis a unit vector ?

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  3. The expression (1/(sqrt(2))hat(i)+1/(sqrt(2))hat(j)) is a

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  4. Vector P=6hati+4sqrt(2)hatj+sqrt(2)hatk makes angle from Z-axas equal ...

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  5. Given A=hat(i)+hat(j)+hat(k)andB=-hat(i)-hat(j)-hat(k) then (A-B) wil...

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  6. If three vectors along coordinate axis represent the adjacent sides of...

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  7. If two vectors are equal and their resultant is also equal to one of t...

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  8. If A and B are two non- zero vectors having equal magnitude, then angl...

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  9. A man first moves 3m due east, then 6m due north and finally 7m due we...

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  10. The resultant of two forces 3P and 2P is R. If the first force is doub...

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  11. The resultant of A and B is R(1) On reversing the vector B , the resul...

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  12. If the sum of two unit vectors is a unit vector, then magnitude of dif...

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  13. In the figure shown, ABCDEF is a regular hexagon. What is the value of...

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  14. Figure shows three vectors p,q and r, where C is the mid-point of AB. ...

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  15. The velocity of a particle is v=6hat(i)+2hat(j)-2hat(k). The componen...

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  16. The resultant R of vector P andQ is perpendicular to P and R=P both ,...

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  17. The value of hat(i)xx(hat(i)xxa)+hat(j)xx(hat(j)xxa)+hat(k)xx(hat(k)xx...

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  18. What is the angle between vec(P) and the resultant of (vec(P)+vec(Q)) ...

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  19. If a(1) and a(2) aare two non- collineaar unit vectors and if |a(1)+a(...

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  20. If theta is the abgle between two vectors A and B , then match the fol...

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