Question

Match List I with List II. 

Choose the correct answer from the options given below : 
 

• (a) $\to$ (iv), (b) $\to$ (iii), (c) $\to$ (i), (d) $\to$ (ii)
• (a) $\to$ (iii), (b) $\to$ (ii), (c) $\to$ (iv), (d) $\to$ (i)
• (a) $\to$ (iv), (b) $\to$ (i), (c) $\to$ (iii), (d) $\to$ (ii)
• (a) $\to$ (i), (b) $\to$ (ii), (c) $\to$ (iii), (d) $\to$ (iv)

Hint:

The vector that goes from the tail of the first to the head of the last is the sum. If you can walk around the whole triangle without ever meeting a head-to-head or tail-to-tail junction, the sum is zero.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Vector addition using the Triangle Law: If two vectors are represented by two sides of a triangle in order (head to tail), the third side taken in the opposite order represents the resultant (sum).
If all three vectors are in order (forming a cycle), their sum is zero.
Step 2: Key Formula or Approach:
Rearrange each equation to identify the resultant:
1. \(\vec{C} = \vec{A} + \vec{B}\)
2. \(\vec{A} = \vec{B} + \vec{C}\)
3. \(\vec{B} = \vec{A} + \vec{C}\)
4. \(\vec{A} + \vec{B} + \vec{C} = 0\)
Step 3: Detailed Explanation:
(a) \(\vec{C} - \vec{A} - \vec{B} = 0 \implies \vec{C} = \vec{A} + \vec{B}\). In diagram (i), \(\vec{A}\) and \(\vec{B}\) are in order, and \(\vec{C}\) is the closing side in the opposite order.
(b) \(\vec{A} - \vec{C} - \vec{B} = 0 \implies \vec{A} = \vec{B} + \vec{C}\). In diagram (ii), \(\vec{B}\) and \(\vec{C}\) are in order, and \(\vec{A}\) is the resultant.
(c) \(\vec{B} - \vec{A} - \vec{C} = 0 \implies \vec{B} = \vec{A} + \vec{C}\). In diagram (iii), \(\vec{A}\) and \(\vec{C}\) are in order, and \(\vec{B}\) is the resultant.
(d) \(\vec{A} + \vec{B} = -\vec{C} \implies \vec{A} + \vec{B} + \vec{C} = 0\). In diagram (iv), all vectors are in a continuous head-to-tail cycle.
Step 4: Final Answer:
The matching sequence is (a) \(\to\) (i), (b) \(\to\) (ii), (c) \(\to\) (iii), (d) \(\to\) (iv).