In order to calculate the resultant vector, you will need to use the trigonometric functions of sine, cosine, and tangent. Start by finding the horizontal and vertical components of each given vector. Then, use the angle between the two vectors to determine the angle of the resultant vector. Finally, use the trigonometric functions to calculate the magnitude and direction of the resultant vector.
The formula for calculating the magnitude of the resultant vector is the square root of the sum of the squares of the horizontal and vertical components of the vector. This can also be written as the square root of (x2 + y2), where x and y are the horizontal and vertical components, respectively.
The direction of the resultant vector can be determined by using the inverse tangent (arctan) function. This will give you the angle between the horizontal component of the resultant vector and the resultant vector itself. Remember to also consider the direction of the given vectors when determining the direction of the resultant vector.
Yes, you can use the Pythagorean theorem to calculate the magnitude of the resultant vector. This is because the Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the horizontal and vertical components of the resultant vector represent the other two sides of the triangle.
If you are given more than two vectors, you will need to first find the resultant vector of the first two vectors using the above method. Then, you can use this resultant vector and the third vector to calculate the final resultant vector. Continue this process for any additional vectors until you have calculated the final resultant vector.