JEE PYQ: Vector Algebra - Question ID 3dad6b1c3aa2 (JEE Main 2023)

In vector algebra, subtraction of two vectors is performed component-wise. If we have two vectors:

then the subtraction $\vec{B} - \vec{A}$ is defined as:

The magnitude of a vector $\vec{V} = V_x \hat{i} + V_y \hat{j} + V_z \hat{k}$ is given by:

Given:

We are told that when $\vec{A}$ is subtracted from $\vec{B}$, the result is $2 \hat{j}$. Mathematically:

Rearranging to solve for $\vec{B}$:

Substitute $\vec{A}$:

Combine like terms:

Now, compute the magnitude of $\vec{B}$:

1. Misinterpreting the subtraction order: Students often confuse $\vec{B} - \vec{A}$ with $\vec{A} - \vec{B}$. Always ensure the order of subtraction matches the problem statement. 2. Forgetting to add components correctly: When solving for $\vec{B}$, ensure all components of $\vec{A}$ are accounted for before adding the resultant vector. 3. Magnitude calculation errors: Squaring negative components or miscounting terms in the magnitude formula can lead to incorrect results. Double-check arithmetic. 4. Exam Tip: Always write down the vector components explicitly before performing operations. This minimizes errors and makes the solution clearer.