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Let two non-collinear unit vectors `veca and vecb` form an acute angle. A point P moves so that at any time t, time position vector, `vec(OP)` ( where O is the origin) is given by `hata cot t + hatb sin t`. When p is farthest fro origing o, let M be the length of `vec(OP) and hatu` be the unit vector along `vec(OP)` .then

A

`hat(u)=(hat(a)+hat(b))/(|hat(a)+hat(b)|) and M=(1+hat(a)*hat(b))^((1)/(2))`

B

`hat(u)=(hat(a)-hat(b))/(|hat(a)-hat(b)|) and M=(1+hat(a)*hat(b))^((1)/(2))`

C

`hat(u)=(hat(a)+hat(b))/(|hat(a)+hat(b)|) and M=(1+2hat(a)*hat(b))^((1)/(2))`

D

`hat(u)=(hat(a)-hat(b))/(|hat(a)-hat(b)|) and M=(1+2hat(a)*hat(b))^((1)/(2))`

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The correct Answer is:
A
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ARIHANT MATHS ENGLISH-PRODUCT OF VECTORS-Exercise (Questions Asked In Previous 13 Years Exam)
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  8. Let vec a= hat i+2 hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec...

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  9. The unit vector which is orthogonal to the vector 3hati+2hatj+6hatk an...

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  10. The value of a so that the volume of parallelepiped formed by hat i...

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  13. If veca and vecb are two unit vectors such that veca + 2vecb and 5 vec...

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  15. If [axxb bxxc c xxa]=lambda[abc]^(2), then lambda is equal to

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  16. Let hata and hatb be two unit vectors. If the vectors vecc=hata+2hatb ...

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  17. Let ABCD be a parallelogram such that vec A B= vec q , vec A D= vec p...

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