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10. vector algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths10. vector algebra1 Mark
MCQ
Let $a = i$ be a vector which makes an angle of ${120^o}$ with a unit vector $b$  Then the unit vector $(a + b)$ is
  • A
    $ - \frac{1}{2}i + \frac{{\sqrt 3 }}{2}j$
  • B
    $ - \frac{{\sqrt 3 }}{2}i + \frac{1}{2}j$
  • ✓
    $\frac{1}{2}i + \frac{{\sqrt 3 }}{2}j$
  • D
    $\frac{{\sqrt 3 }}{2}i - \frac{1}{2}j$
✓

Answer

Correct option: C.
$\frac{1}{2}i + \frac{{\sqrt 3 }}{2}j$
c
(c) $b = \cos 120^\circ i + \sin 120^\circ j$ or $b = - \frac{1}{2}i + \frac{{\sqrt 3 }}{2}j.$

Therefore $a + b = i - \frac{1}{2}i + \frac{{\sqrt 3 }}{2}j = \frac{1}{2}i + \frac{{\sqrt 3 }}{2}j$.

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