Two vectors are at right angle to each other as shown. Find the resultant vector (the sum of the two vectors).

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To find the resultant vector of two vectors that are at right angles to each other, you can use the Pythagorean theorem. Let's say the two vectors are A and B.

1. Draw a diagram representing the two vectors. Label them as vector A and vector B, respectively.
2. Determine the magnitudes (lengths) of vector A and vector B. You can measure them directly from the diagram or use any given values.
3. Use the Pythagorean theorem to find the magnitude of the resultant vector. According to the theorem, the magnitude of the resultant vector (R) can be found using the formula R² = A² + B².
4. Substitute the values of A and B into the equation and solve for R. Take the square root of both sides to find the magnitude of the resultant vector, R.

Now, to find the direction of the resultant vector, you can use trigonometry.

5. Identify the angle between vector A and vector B. In this case, since they are at right angles to each other, the angle is 90 degrees.
6. If vector A makes an angle α with the x-axis, then the angle between the resultant vector and the x-axis can be found using the formula θ = tan⁻¹(B/A). This formula calculates the angle between the resultant vector and vector A.
7. Add 90 degrees to θ to get the angle between the resultant vector and the positive x-axis.

By following these steps, you should be able to find both the magnitude and direction of the resultant vector.