Let two non-collinear unit vectors a^{\^} and b^{\^} form an acute angle. A point P moves so that at any time t the position vector \overrightarrow{OP} (where O is the origin) is given by a^{\^} cos t + b^{\^} sin t. When P is farthest from origin O, let M be the length of \overrightarrow{OP} and u^{\^} be the unit vector along \overrightarrow{OP} Then, [JEE Adv 2008 P2]

Correct Answer is : ^u = ^a+^b|^a+^b| and M = (1+^a.^b)12

u^{\^} = {a^{\^}+b^{\^}}/{|a^{\^}+b^{\^}|} and M = (1+a^{\^}.b^{\^})^{1/2}

u^{\^} = {a^{\^}-b^{\^}}/{|a^{\^}-b^{\^}|} and M = (1+a^{\^}.b^{\^})^{1/2}

u^{\^} = {a^{\^}+b^{\^}}/{|a^{\^}+b^{\^}|} and M = (1+2a^{\^}.b^{\^})^{1/2}

u^{\^} = {a^{\^}-b^{\^}}/{|a^{\^}-b^{\^}|} and M = (1+2a^{\^}.b^{\^})^{1/2}

Vector Algebra

Section: Mathematics

Question : 35 of 38

Marks: +1, -0

Let two non-collinear unit vectors

and

form an acute angle. A point P moves so that at any time t the position vector

→

(where O is the origin) is given by

cos t +

sin t. When P is farthest from origin O, let M be the length of

→

and

be the unit vector along

→

Then,

[JEE Adv 2008 P2]

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