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To find the resultant vector through the Pythagorean theorem, you first need to break down the vectors into their horizontal and vertical components. Then, square each component, add them together, and take the square root of the sum. This will give you the magnitude of the resultant vector. Lastly, use trigonometry to determine the direction of the resultant vector by finding the angle it makes with one of the axes.
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EzraConsider vectors A and B.
A has magnitude s and makes an angle a with the positive direction of the x-axis.
B has magnitude t and makes an angle b with the positive direction of the x-axis.
Then the components of A and B along the x-axis are, respectively, s*cos(a) and t*cos(b).
Thus the total horizontal component is u = s*cos(a) and t*cos(b).
The components of A and B along the y-axis are, respectively, s*sin(a) and t*sin(b).
Thus the total vertical component is v = s*sin(a) and t*sin(b).
The magnitude of the resultant, by Pythagoras, is then sqrt(u2 + v2)
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How do you solve for Equilibrant force?
To solve for the equilibrant force in a system of forces, you must first determine the resultant force by adding all the individual forces acting on an object using vector addition. The equilibrant force is equal in magnitude but opposite in direction to the resultant force. Mathematically, you can find the equilibrant force by multiplying the magnitude of the resultant force by -1 and finding the vector in the opposite direction.
What will happen if all components of a vector are reversed in direction?
Then the resultant vector is reversed.
How can you use the pythagorean theorem to add two vectors that are perpindicular to each other?
Construct the rectangle that contains the right angle subtended by the vectors. Calculate or construct the diagonal of the rectangle. The diagonal is the hypotenuse of a right triangle with the two vectors as sides. The hypotenuse is also the vector that is the sum of the two original vectors. Calculate the magnitude of that vector by applying the theorem.
What are the ways of determining the resultant vector?
You can do it graphically by drawing the vectors with the end of the first touching the beginning of the second, the end of the second touching the beginning of the third, and so on, being careful to maintain the direction and the scale of the magnitude of each. The resultant is then the vector that starts at the beginning of the first vector and ends at the end of the last vector. You should get the same resultant no matter what order you put the vectors in. You can do it matematically by trigonometrically separating each vector into its x and y components, adding together all the x's and adding together all the y's, then calculating the resultant. Think of each vector as the hypotenuse of a right triangle. After adding together the x's and y's, the two sums are the two sides of a right triangle whose hypotenuse is the resultant.
What is vector and resultant velocity?
A vector is used to represent direction and magnitude of speed. Velocity is the speed of an object and a specification of its direction of motion. Speed describes only how fast an object is moving, whereas velocity gives both how fast and in what direction the object is moving. Therefore a vector can be used to represent a velocity. The term "resultant velocity" implies a change in velocity which can be determined using vector analysis.
