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If hat(a) is a unit vector and projectio...

If `hat(a)` is a unit vector and projection of x along `hat(a)` is 2 units and `(hat(a)times x)+b=x,` then x is equal to

A

`(1)/(2)(hat(a)-b+(hatatimesb))`

B

`(1)/(2)(2hat(a)+b+(hatatimesb))`

C

`(hat(a)+(hatatimesb))`

D

None of these

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The correct Answer is:
B
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ARIHANT MATHS-PRODUCT OF VECTORS-Exercise (Single Option Correct Type Questions)
  1. If vector vec i+ 2vec j + 2vec k is rotated through an angle of 90^@...

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  2. 10 different vectors are lying on a plane out of which four are parall...

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  3. If hat(a) is a unit vector and projection of x along hat(a) is 2 units...

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  4. If a, b and c are any three non-zero vectors, then the component of at...

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  5. The position vector of a point P is r=xhat(i)+yhat(j)+hat(k)z, where x...

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  6. . Let a, b > 0 and vecalpha=hati/a+4hatj/b+bhatk and beta=bhati+ahatj+...

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  7. If veca, vecb and vecc are any three vectors forming a linearly indepe...

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  8. Two adjacent sides of a parallelogram ABCD are given by vec(AB)=2hati+...

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  9. If in a triangleABC, BC=(e)/(|e|)-(f)/(|f|) and AC=(2e)/(|e|): |e|ne|f...

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  10. Let the unit vectors a and b be perpendicular and the unit vector c be...

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  11. In triangle ABC the mid point of the sides AB, BC and AC respectively ...

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  12. The angle between the lines whose directionn cosines are given by 2l-m...

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  13. A line makes an angle theta both with x-axis and y-axis. A possible ra...

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  14. Let veca, vecb and vecc be the three vectors having magnitudes, 1,5 an...

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  15. Find the perpendicular distance of a corner of a unit cube from a dia...

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  16. If p,q are two-collinear vectors such that (b-c)ptimesq+(c-a)p+(a-b)q...

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  17. Let a=hat(i)+hat(j)+hat(k), b=-hat(i)+hat(j)+hat(k), c=hat(i)-hat(j)+h...

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  18. A parallelepiped is formed by planes drawn parallel to coordinate axes...

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  19. Let bar a,bar b,bar c be three non-coplanar vectors and bar d be a no...

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  20. If alpha(atimesb)+beta(btimesc)+gamma(ctimesa)=0, then

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