Let two non−collinear unit vectors a^{\^} and b^{\^} form an acute angle. A point P moves so that at any time tthe position vector \stackrel{––––}{OP} (where O is the origin) is given by a^{\^} cost + b^{\^} sint. When P is farthest fromorigin O, let M be the length of \stackrel{––––}{OP} and u^{\^} be the unit vector along \stackrel{––––}{OP} . Then,

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}

JEE Mains Model Paper 19

Question : 56 of 90

Marks: +1, -0

Let two non−collinear unit vectors

and

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

––––

(where O is the origin) is given by

cost +

sint. When P is farthest fromorigin O, let M be the length of

––––

and

be the unit vector along

––––

. Then,

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