If overrightarrow A = 4hat i - 3hat j and ove | vedclass

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(B) Given vectors are $\overrightarrow A = 4\hat i - 3\hat j$ and $\overrightarrow B = 6\hat i + 8\hat j$.First,find the resultant vector $\overrighta

Vedclass · Accepted Answer

$5\sqrt{5}, 	an^{-1}(1/2)$

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(B) Given vectors are $\overrightarrow A = 4\hat i - 3\hat j$ and $\overrightarrow B = 6\hat i + 8\hat j$.First,find the resultant vector $\overrightarrow R = \overrightarrow A + \overrightarrow B$:$\overrightarrow R = (4\hat i - 3\hat j) + (6\hat i + 8\hat j) = (4+6)\hat i + (-3+8)\hat j = 10\hat i + 5\hat j$.The magnitude of the resultant vector is given by:$|\overrightarrow R| = \sqrt{(10)^2 + (5)^2} = \sqrt{100 + 25} = \sqrt{125} = 5\sqrt{5}$.The direction $	heta$ with respect to the $x$-axis is given by:$	an 	heta = \frac{R_y}{R_x} = \frac{5}{10} = \frac{1}{2}$.Therefore,$	heta = 	an^{-1}(1/2)$.

If $\overrightarrow A = 4\hat i - 3\hat j$ and $\overrightarrow B = 6\hat i + 8\hat j$,then the magnitude and direction of $\overrightarrow A + \overrightarrow B$ will be:

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