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A vector has magnitude same as that of $$\vec{A} = 3\hat{i} + 4\hat{j}$$ and is parallel to $$\vec{B} = 4\hat{i} + 3\hat{j}$$. The $$x$$ and $$y$$ components of this vector in first quadrant are $$x$$ and 3 respectively where $$x$$ = ____.
Correct Answer: 4
$$|\vec{A}| = \sqrt{9 + 16} = 5$$. $$\vec{B} = 4\hat{i} + 3\hat{j}$$, $$|\vec{B}| = 5$$.
Unit vector along $$\vec{B}$$: $$\hat{B} = \frac{4\hat{i} + 3\hat{j}}{5}$$.
Required vector = $$5\hat{B} = 4\hat{i} + 3\hat{j}$$.
The x-component is 4 and y-component is 3.
Therefore, $$x = \boxed{4}$$.
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