Math Problem Statement
Solution
Let's break down and solve the problem step by step.
Part (a):
The task is to find the diagram that shows the correct addition of vectors and using the tip-to-tail method.
Vector is given as , meaning it has components:
Looking at the diagrams:
- Identify where vector is placed relative to vector . The correct method involves placing the tail of at the tip of .
- The resultant vector should extend from the origin of to the tip of .
We can identify the correct diagram by finding the one that correctly places vector at the tip of .
Part (b):
You need to fill in the table with the x and y components of vectors and , and then find the components of their resultant vector .
Let's first read the components of vector from the graph:
- (since extends from 0 to -4 on the x-axis)
- (since extends from 0 to 3 on the y-axis)
Vector was given as:
Now calculate the components of the resultant vector :
Part (c):
The resultant vector in unit vector notation is:
Would you like further clarification or more details on any part of the solution?
Related Questions:
- How do we apply the tip-to-tail method for adding vectors?
- What are the geometric interpretations of vector components?
- Can we use another method (like the parallelogram method) for vector addition?
- What is the significance of unit-vector notation in vector calculations?
- How can you find the magnitude of the resultant vector from its components?
Tip:
When adding vectors graphically, ensure to always align the vectors tip-to-tail and check the resulting direction and magnitude visually before calculating numerically.
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Math Problem Analysis
Mathematical Concepts
Vector Addition
Unit Vectors
Component Form of Vectors
Formulas
R_x = A_x + D_x
R_y = A_y + D_y
Vector in unit form: R = R_x i + R_y j
Theorems
Tip-to-Tail Vector Addition
Suitable Grade Level
Grades 10-12
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