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:
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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....
