A vector has magnitude same as that of and is parallel to . The and components of this vector in first quadrant are and 3 respectively where x

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Solution

Q.
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 $x =$ _________ . [2024]

Ans.
(4) Given $\vec{A} = 3 i + 4 j,$ $\vec{B} = 4 i + 3 j,$

$| A | = \sqrt{3^{2} + 4^{2}} = 5,$ $\hat{B} = \frac{4 i + 3 j}{5}, \frac{\vec{B}}{| B |} = \hat{B}$

Now, as per question, $\vec{C} = | A | \hat{B},$ mag of $\vec{A}$ and direction of B

$= (5) \frac{(4 i + 3 j)}{5} = 4 i + 3 j, 4 i + 3 j,$ $∴ x = 4$

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