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3.1 vectors — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics3.1 vectors1 Mark
MCQ
If $\overrightarrow A = 4\hat i - 3\hat j$ and $\overrightarrow B = 6\hat i + 8\hat j$ then magnitude and direction of $\overrightarrow A \, + \overrightarrow B $ will be
  • A
    $5,\,{\tan ^{ - 1}}(3/4)$
  • ✓
    $5\sqrt 5 ,{\tan ^{ - 1}}(1/2)$
  • C
    $10,\,{\tan ^{ - 1}}(5)$
  • D
    $25,\,{\tan ^{ - 1}}(3/4)$
✓

Answer

Correct option: B.
$5\sqrt 5 ,{\tan ^{ - 1}}(1/2)$
b
(b) $\overrightarrow A + \overrightarrow B = 4\hat i - 3\hat j + 6\hat i + 8\hat j\,\, = 10\hat i + 5\hat j$

$|\overrightarrow A + \overrightarrow B |\, = \,\sqrt {{{(10)}^2} + {{(5)}^2}} $ $ = \,5\sqrt 5 $

$\tan \theta = \frac{5}{{10}} = \frac{1}{2}$ $ \Rightarrow $$\theta = {\tan ^{ - 1}}\left( {\frac{1}{2}} \right)$

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