Verified Solution • 2025–26 Session
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Q3.19: NCERT Physics - Part 1 MOTION IN A PLANE 3.19 Solution: i and j are unit vectors along x- and y-axis respectively. What …
⚠️ Common Exam Traps & Conceptual Pitfalls
When projecting a vector onto $\mathbf{i}+\mathbf{j}$ or $\mathbf{i}-\mathbf{j}$, many students use the dot product $\mathbf{A}\cdot(\mathbf{i}\pm\mathbf{j})$ and stop at $5$ or $-1$, forgetting that $\mathbf{i}\pm\mathbf{j}$ is not a unit vector. The correct scalar component is the dot product divided by $|\mathbf{i}\pm\mathbf{j}|=\sqrt{2}$, giving $5/\sqrt{2}$ and $-1/\sqrt{2}$ respectively. Always normalize the direction vector before reporting the component magnitude.
i and j are unit vectors along x- and y-axis respectively. What is the magnitude and direction of the vectors i + j, and i _ j? What are the components of a vector A = 2i + 3j along the directions of i + j and i _ j? [You may use graphical method]
Step-by-Step Verified Solution
**Answer:** |i+j| = �2, direction 45�. |i_j| = �2, direction _45�. Components: along i+j = 5/�2, along i_j = _1/�2.
**Step-by-Step Explanation:**
i+j: magnitude �2, angle 45� from x-axis. i_j: magnitude �2, angle _45�.
A = 2i + 3j. Component along (i+j): (2+3)/�2 = 5/�2. Component along (i_j): (2_3)/�2 = _1/�2.
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