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
$5,\,{\tan ^{ - 1}}(3/4)$
$5\sqrt 5 ,{\tan ^{ - 1}}(1/2)$
$10,\,{\tan ^{ - 1}}(5)$
$25,\,{\tan ^{ - 1}}(3/4)$
If two vectors $\vec{A}$ and $\vec{B}$ having equal magnitude $\mathrm{R}$ are inclined at an angle $\theta$, then
Match List$- I$ with List$- II.$
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Choose the correct answer from the options given below :
The vectors $\overrightarrow A $ and $\overrightarrow B$ lie in a plane. Another vector $\overrightarrow C $ lies outside this plane. The resultant $\overrightarrow A + \overrightarrow B + \overrightarrow C$ of these three vectors
What displacement must be added to the displacement $25\hat i - 6\hat j\,\,m$ to give a displacement of $7.0\, m$ pointing in the $X- $direction