Published by:
CGP EDU Academic Team
Published on: September 12, 2026
Any vector in an arbitrary direction can always be replaced by two (or three)
Text Solution
Verified by ExpertsThe correct answer is:
C
Resolution of a Vector:
The process of splitting a single vector into two or more vectors is known as vector resolution.
Therefore, any vector can always be replaced by arbitrary vectors which have the original vector as their resultant.
Correct Answer: Option C
The process of splitting a single vector into two or more vectors is known as vector resolution.
- Any vector $\vec{R}$ in a plane can be resolved into two arbitrary (non-parallel) vectors $\vec{A}$ and $\vec{B}$ such that their vector sum equals the original vector: $$\vec{R} = \vec{A} + \vec{B}$$
- Similarly, in three-dimensional space, any vector can be resolved into three arbitrary (non-coplanar) vectors whose resultant is the original vector.
- While resolving a vector into mutually perpendicular (rectangular) components is very common and convenient, it is not a restriction; the directions can be completely arbitrary as long as they span the vector space.
Therefore, any vector can always be replaced by arbitrary vectors which have the original vector as their resultant.
Correct Answer: Option C
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