what are the components i and j of a vector with initial point -1;-3 and terminal point 2;1

The components \( i \) and \( j \) of a vector can be found by calculating the differences between the coordinates of the terminal point and the initial point. Let's denote the initial point as \( A(-1, -3) \) and the terminal point as \( B(2, 1) \).

To find the components of the vector, use the following formulas:

\[
i = x_2 - x_1
\]
\[
j = y_2 - y_1
\]

where:
- \( x_1 \) and \( y_1 \) are the coordinates of the initial point \( A(-1, -3) \).
- \( x_2 \) and \( y_2 \) are the coordinates of the terminal point \( B(2, 1) \).

Substituting the values:
\[
i = 2 - (-1) = 2 + 1 = 3
\]
\[
j = 1 - (-3) = 1 + 3 = 4
\]

So, the vector components are:
\[
\text{Vector} = 3i + 4j
\]

Would you like a detailed explanation of how these calculations were performed or have any questions about the process?

Here are some related questions you might find useful:
1. How do you find the magnitude of a vector given its components?
2. What is the difference between vector notation and component form?
3. How do you add two vectors using their components?
4. How do you calculate the direction of a vector from its components?
5. What are unit vectors and how are they calculated?

**Tip:** Remember that vector components can be seen as coordinates showing how far the vector moves in the \( x \) (horizontal) and \( y \) (vertical) directions.

What are the components i and j of a vector with initial point -1, -3 and terminal point 2, 1?

Find the components of a vector given initial point (-1, -3) and terminal point (2, 1). Learn how to calculate the i and j components using vector analysis in coordinate geometry, suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation