Introduction:

In physics, vectors are quantities that have both magnitude and direction. To analyze vectors, we often break them down into their vector components. This is useful in many situations, such as when we need to determine the force acting on an object in a specific direction.

Given:

The vector components of a vector are 2i and 3j. We are asked to find the direction of the vector in terms of i and j.

Explanation:

To understand the direction of the vector in terms of i and j, we need to first understand what i and j represent.

- i represents the unit vector in the x-direction.
- j represents the unit vector in the y-direction.

This means that any vector can be represented as a sum of its x-component and y-component, where the x-component is multiplied by i and the y-component is multiplied by j.

So, if the vector components are 2i and 3j, we can represent the vector as:

- 2i + 3j

To find the direction of this vector, we need to determine the angle it makes with the x-axis. We can do this using trigonometry.

- tan(theta) = (3)/(2)
- theta = tan^-1(3/2)

Therefore, the direction of the vector in terms of i and j is:

- 2i + 3j cap along the direction of i j

Conclusion:

In conclusion, to find the direction of a vector in terms of i and j, we need to break the vector down into its vector components and use trigonometry to determine the angle it makes with the x-axis. This is useful in many situations where we need to analyze the force acting on an object in a specific direction.

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