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3-1.Vectors
medium
$\overrightarrow A = 4\hat i - 3\hat j$ અને $\overrightarrow B = 6\hat i + 8\hat j$ હોય તો , $\overrightarrow A \, + \overrightarrow B $ નુ મુલ્ય અને દિશા મેળવો.
A
$5,\,{\tan ^{ - 1}}(3/4)$
B
$5\sqrt 5 ,{\tan ^{ - 1}}(1/2)$
C
$10,\,{\tan ^{ - 1}}(5)$
D
$25,\,{\tan ^{ - 1}}(3/4)$
Solution
$\overrightarrow A + \overrightarrow B = 4\hat i – 3\hat j + 6\hat i + 8\hat j\,\, = 10\hat i + 5\hat j$
$|\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)$
Standard 11
Physics
