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10. vector algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths10. vector algebra1 Mark
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
    $3 i +5 j +\frac{8}{5} k$
✓

Answer

Correct option: B.
$39 i +25 j +8 k$
b
(b)

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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