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Let two non-collinear unit vectors hat(a...

Let two non-collinear unit vectors `hat(a)` and `hat(b)` form an acute angle. A point P moves so that at any time t, the position vector `vec(OP)` (where O is the origin) is given by `hat(a)cott+hat(b) sin t` . When P is farthest from origin O, let M be the length of `vec(OP)` and `vec(u)` 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)`

Text Solution

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The correct Answer is:
A
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