MCQ
A vector which bisects the angle between $a =3 i -4 k$ and $b =5 j +12 k$ is
- A$39 i -25 j +8 k$
- ✓$39 i +25 j +8 k$
- C$3 i -5 j +\frac{8}{5} k$
- D$3 i +5 j +\frac{8}{5} k$
We have,
$a =3 i -4 k$ and $b =5 j +12 k$
We know that,
angle bisector of vector $a$ and $b$
$=\lambda\left[\frac{ a }{| a |}+\frac{ b }{| b |}\right]$
$\therefore \lambda\left[\frac{3 \hat{ i }-4 \hat{ k }}{5}+\frac{5 \hat{ j }+12 \hat{ k }}{13}\right]$
$=\lambda\left[\frac{39 \hat{ i }-52 \hat{ k }+25 \hat{ j }+60 \hat{ k }}{65}\right]$
$=\lambda[39 \hat{ i }+2 \hat{ j}+8 \hat{ k }]$
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