Question

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

Accepted Answer

${\bf{\hat u}} = \frac{{{\bf{\hat a}} + {\bf{\hat b}}}}{{\left| {{\bf{\hat a}} + {\bf{\hat b}}} \right|}}{\rm{and\;}}M = {(1 + {\bf{\hat a}}\cdot{\bf{\hat b}})^{1/2}}$

Answer

${\bf{\hat u}} = \frac{{{\bf{\hat a}} - {\bf{\hat b}}}}{{\left| {{\bf{\hat a}} - {\bf{\hat b}}} \right|}}{\rm{and\;}}M = {(1 + {\bf{\hat a}}\cdot{\bf{\hat b}})^{1/2}}$

Answer

${\bf{\hat u}} = \frac{{{\bf{\hat a}} + {\bf{\hat b}}}}{{\left| {{\bf{\hat a}} + {\bf{\hat b}}} \right|}}{\rm{and\;}}M = {(1 + 2{\bf{\hat a}}\cdot{\bf{\hat b}})^{1/2}}$

Answer

${\bf{\hat u}} = \frac{{{\bf{\hat a}} - {\bf{\hat b}}}}{{\left| {{\bf{\hat a}} - {\bf{\hat b}}} \right|}}{\rm{and\;}}M = {(1 + 2{\bf{\hat a}}\cdot{\bf{\hat b}})^{1/2}}$

JEE MATHEMATICS MCQ: ADDITION OF VECTORS

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