Given the displacement vector D = (3.30
i - 5.40
j)m, find the displacement vector R so that D + R = −4.00
D
j.



Part 1 +

Which expression below shows a correct algebraic expression for the resultant vector R?

Enter correct letter: 
c

Correct answer, well done.
Marks for this submission: 0.250/0.250.
a. −5.00
D
j

b. (3.30
i −
 5.40
j)m −4.00
D
j

c. (−3.30
i +
 5.40
j)m −4.00
D
j

d. (−3.30
i +
 5.40
j)m +
4.00
D
j



Part 2

Find the displacement vector R.

-3.30 m
 i

Correct answer, well done.
Marks for this submission: 0.500/0.500.


 j

To break down the problem and solution:

### Part 1: Algebraic Expression for the Resultant Vector \( R \)

Given:
- Displacement vector \( D = (3.30 \hat{i} - 5.40 \hat{j}) \, m \)
- The relationship \( D + R = -4.00 D_j \)

We are tasked with finding the correct algebraic expression for the resultant vector \( R \). 

The correct option is **(c)**:
\[
R = (-3.30 \hat{i} + 5.40 \hat{j}) \, m - 4.00 D_j
\]
This means we reverse the \( \hat{i} \)-component (changing it to \(-3.30 \hat{i}\)) and adjust the \( \hat{j} \)-component accordingly.

### Part 2: Find the Displacement Vector \( R \)

From the expression \( D + R = -4.00 D_j \), we need to solve for \( R \).

1. The displacement vector \( D = (3.30 \hat{i} - 5.40 \hat{j}) \, m \).
2. The resultant vector given by \( -4.00 D_j \) modifies the \( \hat{j} \)-component to:
   \[
   -4.00 D_j = -4.00 \times (-5.40 \hat{j}) = 21.6 \hat{j}
   \]
3. Now, \( D + R = -4.00 D_j \), so:
   \[
   (3.30 \hat{i} - 5.40 \hat{j}) + R = 21.6 \hat{j}
   \]
   Solving for \( R \), we get:
   \[
   R = (-3.30 \hat{i} + 21.6 \hat{j})
   \]
Thus, the displacement vector \( R \) is:
\[
R = (-3.30 \hat{i} + 21.6 \hat{j}) \, m
\]

---

Let me know if you'd like more details or if you have any questions!

Here are 5 related questions for practice:
1. What is the magnitude of the vector \( D = (3.30 \hat{i} - 5.40 \hat{j}) \)?
2. If \( D + R = 0 \), what would the vector \( R \) be?
3. How do you find the magnitude of the vector \( R \)?
4. If the vector \( D \) was rotated 90 degrees, what would its new components be?
5. What is the direction of the resultant vector \( R \)?

**Tip:** To find the magnitude of a vector, use the formula \( \sqrt{x^2 + y^2} \), where \( x \) and \( y \) are the components of the vector.

Given the displacement vector D = (3.30 i - 5.40 j) m, find the displacement vector R so that D + R = −4.00 D_j.

Learn how to find the displacement vector R when given the vector D = (3.30 i - 5.40 j) m and the equation D + R = −4.00 D_j. This problem covers vector addition and the manipulation of vector components in algebraic form. Suitable for high school students in Grades 9-12.

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