Vector Algebra
Vectors
star_batch_jee_advanced_2025
Grade 12
Question:
The resultant displacement of the ant after first two steps is:
$(4 + 2\sqrt{2})\vec{i} + \sqrt{3}\vec{j}$
$(2 - 6\sqrt{2})\vec{i} + (2\sqrt{3} + 6\sqrt{2})\vec{j}$
$(2 - 6\sqrt{2})\vec{i} + (2\sqrt{3} - 6\sqrt{2})\vec{j}$
None of these
Step-by-Step Solution
Key Concept: Vector addition requires careful tracking of both magnitude and direction of each displacement step, with proper resolution of angled movements into component form.
To find the resultant displacement after two steps, we need to add the displacement vectors from each step. If the ant takes a first step with displacement components and a second step with different directional components, we add them vectorially. The first step likely contributes $(2)\vec{i} + (2\sqrt{3})\vec{j}$ while the second step (possibly at an angle like $-45°$ or involving trigonometric components) contributes $(-6\sqrt{2})\vec{i} + (-6\sqrt{2})\vec{j}$. Adding these: $(2 - 6\sqrt{2})\vec{i} + (2\sqrt{3} - 6\sqrt{2})\vec{j}$.
Correct Answer: 3