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When finding your resultant vector for a-d you were using the graphical method of resolving vectors. However, you could solve using more direct mathematical equations. Give the formula and explain how you would find the resultant vector’s magnitude using these calculations.



Answer :

Answer:

To find the magnitude of the resultant vector using direct mathematical equations, you typically use vector addition and the Pythagorean theorem for two-dimensional vectors. Here’s how you can do it:

### Formula for Resultant Vector

Given two vectors \(\mathbf{A}\) and \(\mathbf{B}\) with components:

\[ \mathbf{A} = (A_x, A_y) \]

\[ \mathbf{B} = (B_x, B_y) \]

The resultant vector \(\mathbf{R}\) is the sum of \(\mathbf{A}\) and \(\mathbf{B}\):

\[ \mathbf{R} = \mathbf{A} + \mathbf{B} \]

\[ \mathbf{R} = (A_x + B_x, A_y + B_y) \]

### Magnitude of the Resultant Vector

To find the magnitude of the resultant vector \(\mathbf{R}\), use the Pythagorean theorem:

\[ R = \sqrt{(A_x + B_x)^2 + (A_y + B_y)^2} \]

### Example Calculation

Suppose you have the following vectors:

\[ \mathbf{A} = (3, 4) \]

\[ \mathbf{B} = (1, 2) \]

First, find the components of the resultant vector \(\mathbf{R}\):

\[ \mathbf{R} = (3 + 1, 4 + 2) \]

\[ \mathbf{R} = (4, 6) \]

Next, calculate the magnitude \(R\):

\[ R = \sqrt{(4)^2 + (6)^2} \]

\[ R = \sqrt{16 + 36} \]

\[ R = \sqrt{52} \]

\[ R = 2\sqrt{13} \]

Therefore, the magnitude of the resultant vector is \(2\sqrt{13}\).

### Summary

1. **Resolve the vectors into their components**.

2. **Add the corresponding components** to find the resultant vector’s components.

3. **Use the Pythagorean theorem** to find the magnitude of the resultant vector.

Explanation:

if you like it thank you

Answer:

Formula for magnitude of resultant vector=

|R|=a^2+d^2+2 a d cos theta.

Explanation:

| a + d |= √(a^2 +d^2+ 2adcostheta) {where theta the angle between the two component vectors}.

I hope that this answer will help you....