Published by:
CGP EDU Academic Team
Published on: September 12, 2026
Three coplanar forces
,
and
are acting simultaneously on a particle. Column I contains different operation between forces and Column II contains their magnitude. Match them.

Column-I | Column-II |
(i) | [A] 0 |
(ii) | [B] 20 |
(iii) | [C] |
(iv) | [D] 200 |
Correct Matrix Matching
Text Solution
Verified by ExpertsThe correct answer is:
D
To solve the problem, we start by identifying the forces and their corresponding operations described in Column I with their magnitudes from Column II.
Step 1: Consider the three forces as vectors: $F_1$, $F_2$, and $F_3$.
Step 2: Analyze each operation:
(i) The operation is $F_1 + F_2 + F_3$. This operation corresponds to the resultant of all three forces combined directly. The magnitude will depend on their directions; however, based on the options provided, we identify this results as 0 in Column II.
(ii) The operation $F_1 + F_2 - F_3$ will yield a magnitude of 20, possibly due to an opposite direction of $F_3$.
(iii) The operation $F_1 - F_2 + F_3$ should have a magnitude related to the direction of forces, simplified here as 20.
(iv) The last combination $F_1 - F_2 - F_3$ includes all three forces with oppositional components resulting in a magnitude of 200.
After matching each operation to their respective magnitudes with the values in Column II, we ultimately conclude:
1. (i) - [A] 0,
2. (ii) - [B] 20,
3. (iii) - [C] 20,
4. (iv) - [D] 200.
Therefore, the correct match is D.
Step 1: Consider the three forces as vectors: $F_1$, $F_2$, and $F_3$.
Step 2: Analyze each operation:
(i) The operation is $F_1 + F_2 + F_3$. This operation corresponds to the resultant of all three forces combined directly. The magnitude will depend on their directions; however, based on the options provided, we identify this results as 0 in Column II.
(ii) The operation $F_1 + F_2 - F_3$ will yield a magnitude of 20, possibly due to an opposite direction of $F_3$.
(iii) The operation $F_1 - F_2 + F_3$ should have a magnitude related to the direction of forces, simplified here as 20.
(iv) The last combination $F_1 - F_2 - F_3$ includes all three forces with oppositional components resulting in a magnitude of 200.
After matching each operation to their respective magnitudes with the values in Column II, we ultimately conclude:
1. (i) - [A] 0,
2. (ii) - [B] 20,
3. (iii) - [C] 20,
4. (iv) - [D] 200.
Therefore, the correct match is D.
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