ExamHabit
Practise free

AIEEE 2008

JEE Main 2008 Mathematics question on Vector Algebra

Let two non-collinear unit vectors a^\hat{a} and b^\hat{b} form an acute angle. A point PP moves, so that at any time tt the position vector OP→\overrightarrow{OP} (where, OO is the origin) is given by a^cos⁡t+b^sin⁡t\hat{a}\cos t + \hat{b}\sin t. When PP is farthest from origin OO, let MM be the length of OP→\overrightarrow{OP} and u^\hat{u} be the unit vector along OP→\overrightarrow{OP}. Then,
  1. A.
    u^=a^+b^∣a^+b^∣\hat{u} = \dfrac{\hat{a} + \hat{b}}{|\hat{a} + \hat{b}|} and M=(1+a^⋅b^)1/2M = (1 + \hat{a} \cdot \hat{b})^{1/2}
  2. B.
    u^=a^−b^∣a^−b^∣\hat{u} = \dfrac{\hat{a} - \hat{b}}{|\hat{a} - \hat{b}|} and M=(1+a^⋅b^)1/2M = (1 + \hat{a} \cdot \hat{b})^{1/2}
  3. C.
    u^=a^+b^∣a^+b^∣\hat{u} = \dfrac{\hat{a} + \hat{b}}{|\hat{a} + \hat{b}|} and M=(1+2a^⋅b^)1/2M = (1 + 2\hat{a} \cdot \hat{b})^{1/2}
  4. D.
    u^=a^−b^∣a^−b^∣\hat{u} = \dfrac{\hat{a} - \hat{b}}{|\hat{a} - \hat{b}|} and M=(1+2a^⋅b^)1/2M = (1 + 2\hat{a} \cdot \hat{b})^{1/2}
Show answer

Correct option: A

[AIEEE 2008]

Practise Vector Algebra the way it is asked

A timed set of real JEE Main Vector Algebra questions, graded as the exam grades. No sign-up.

Start a Vector Algebra test

More: all JEE Main Vector Algebra questions · JEE Main 2008 · Mathematics chapter list