Q73 / 160 · AP EAMCET 2024 (20 May Shift 1) · Mathematics

If $\vec{a}, \vec{b}$ are the two non collinear vectors. then $|\vec{b}| \vec{a}+|\vec{a}| \vec{b}$ represents

  • Correct answer
    A
    a vector parallel to an angle bisector of $\vec{a}, \vec{b}$
  • B
    a vector along the difference of the vectors $\vec{a}, \vec{b}$
  • C
    a vector along $\vec{a}+\vec{b}$
  • D
    a vector outside the triangle having $\vec{a}, \vec{b}$ as adjacent sides

Solution

$|\overrightarrow{\mathrm{b}}| \vec{a}+|\overrightarrow{\mathrm{a}}| \vec{b}=\frac{1}{|\vec{a}||\vec{b}|}\left[\frac{\vec{a}}{|\vec{a}|}+\frac{\vec{b}}{|\vec{b}|}\right][\because \vec{a} \neq 0, \vec{b} \neq 0]$ $=k[\vec{a}+\vec{b}]$ Which is a vector parallel to an angle bisector of $\vec{a}, \vec{b}$.

Hence, the correct answer is option: 'A'.

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