HallsofIvy said:
songoku said:
Hope that helps.To find the magnitude of a vector in a triangle, you can use the Pythagorean theorem. This theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In a triangle, the magnitude of a vector is equal to the length of the side opposite the angle it forms with the x-axis.
The direction of a vector in a triangle can be found by using the tangent function. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In other words, the direction of a vector is the slope of the line connecting its starting point to its endpoint.
Yes, the components of a vector in a triangle can be found using trigonometric functions. The x-component of a vector can be calculated by multiplying its magnitude by the cosine of the angle it forms with the x-axis. Similarly, the y-component can be found by multiplying the magnitude by the sine of the angle.
Yes, vectors in a triangle can have negative components. This means that the vector is pointing in the opposite direction of the positive axis. However, the magnitude of the vector will always be positive.
The resultant vector in a triangle can be found by adding the x-components and y-components of all the given vectors. This will give you the x-component and y-component of the resultant vector. The magnitude of the resultant vector can then be found using the Pythagorean theorem, and the direction can be calculated using the tangent function.