In how many independent directions can a vector in a plane be resolved?a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer?

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ACT Exam > ACT Questions > In how many independent directions can a vect...

In how many independent directions can a vector in a plane be resolved?

a)
1
b)
2
c)
3
d)
4

Correct answer is option 'B'. Can you explain this answer?

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In how many independent directions can a vector in a plane be resolved...

A vector in a plane will be defined by the two governing axes, X and Y. Hence, any vector can be resolved in two independent directions. If it is resolved in any other direction, that component of it will be dependent on the existing independent directions.

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In how many independent directions can a vector in a plane be resolved...

Understanding Vector Resolution in a Plane
When we talk about resolving a vector in a plane, we refer to breaking it down into its components along specific independent directions.
Independent Directions in a Plane
In a two-dimensional space (or plane), there are two key independent directions:
- Horizontal (x-axis): This represents the direction along the width of the plane.
- Vertical (y-axis): This represents the direction along the height of the plane.
These two directions are perpendicular to each other, meaning they do not affect each other’s measurements, making them independent.
Importance of Resolution
Resolving a vector into its components is crucial for simplifying complex problems in physics and engineering. Each component can be analyzed separately, allowing for:
- Easier calculations: By dealing with two simpler one-dimensional problems instead of one complicated two-dimensional problem.
- Clear understanding: Understanding how a vector behaves in each independent direction.
Conclusion
Thus, in a plane, a vector can be resolved into two independent directions – the horizontal and vertical components. This is why the correct answer to the question is option 'B'.

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