QJEEM24Ph1f6f: JEE Main 2024 Physics - Class 11 JEEM24Ph1f6f Solution: A vector has magnitude same as that of and is parallel to . The …

To find a vector that has the same magnitude as vector $\vec{A}$ and is parallel to vector $\vec{B}$ , we use the formula:

$\vec{N} = |\vec{A}| \hat{B}$

First, let's find the magnitude of $\vec{A}$ , which is $|\vec{A}|$ .

$|\vec{A}| = \sqrt{3^2 + 4^2}=5$

We're given that $\vec{B} = 4 \hat{i}+3 \hat{j}$ , so to make $\vec{N}$ parallel to $\vec{B}$ and have it have the same magnitude as $\vec{A}$ , they should be the same when $\vec{N}$ 's magnitude is divided by 5, since $|\vec{A}|=5$ .

So, $\vec{N} = \frac{5(4\hat{i}+3\hat{j})}{5} = 4\hat{i}+3\hat{j}$ .

This means the $x$ component of the vector in the first quadrant is 4, and the $y$ component is given as 3. So, $x=4$ .