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JEE Main 2024 (30 Jan, Shift 2) · Vector Basics, Unit Vectors & Components

Vector Basics, Unit Vectors & Components question from JEE Main 2024 (30 Jan, Shift 2)

Q10JEE Main 2024 · 30 JAN · SHIFT 2Medium

Vector Basics, Unit Vectors & Components

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 $x =$ _________.

Numerical answer type. Work it out, then open the answer.

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Answer: 4

$|\vec{A}| = \sqrt{9 + 16} = 5$ ; unit vector along $\vec{B}$ is $\frac{4\hat{i} + 3\hat{j}}{5}$ .
Required vector $= 5 \times \frac{4\hat{i} + 3\hat{j}}{5} = 4\hat{i} + 3\hat{j}$
So $x = 4$ .

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