Consider 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)
Then the resultant vector is reversed.
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.
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.
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.
The resultant vector has maximum magnitude if the vectors act in concert. That is, if the angle between them is 0 radians (or degrees). The magnitude of the resultant is the sum of the magnitudes of the vectors.For two vectors, the resultant is a minimum if the vectors act in opposition, that is the angle between them is pi radians (180 degrees). In this case the resultant has a magnitude that is equal to the difference between the two vectors' magnitudes, and it acts in the direction of the larger vector.At all other angles, the resultant vector has intermediate magnitudes.
When drawing a vector using the triangle method you will draw in the resultant vector using Pythagorean theorem. This is taught in physics.
You must find the x and y components of each vector. Then you add up the like x components and the like y components. Using your total x component and total y component you may then apply the pythagorean theorem.
To calculate the magnitude of the resultant vector, you can use the Pythagorean theorem. Square the x-component of the vector, square the y-component of the vector, and sum them together. Finally, take the square root of the resulting sum. The formula is: |R| = sqrt((Rx^2) + (Ry^2)).
No. Vectors add at rightangle bythe pythagoran theorem: resultant sum = square root of (vector 1 squared + vector 2 squared)
The Resultant Vector minus the other vector
The resultant vector describes the complete vector, magnitude and direction; while the component vector describes a single component of a vector, like the x-component. If the resultant vector has only one component, the resultant and the component are the same and there is no difference.t
The resultant vector is the vector that 'results' from adding two or more vectors together. This vector will create some angle with the x -axis and this is the angle of the resultant vector.
the difference between resultant vector and resolution of vector is that the addition of two or more vectors can be represented by a single vector which is termed as a resultant vector. And the decomposition of a vector into its components is called resolution of vectors.
An easy way to visual this is by drawing a triangle with the vectors. Obviously one vector will be the vertical and another will be perpendicular to that, the horizontal. These two vectors will connect at the ends. Then you connect the other two ends with another vector and that is the resultant. Vector sum, or the square root of the sum of the squares; you use the pythagorem theorem to find the resultant, also the hypotenuse. r2= v12 + v22. The vertical vector squared plus the horizontal squared, you take the root of the sum of the squared vectors and that gives the resultant vector. If the horizontal or vertical vector is negative, then the resultant vector will be negative as well. This is used for any units including velocity, distance, and acceleration.
by method of finding resultant
Equilibrant vector is the opposite of resultant vector, they act in opposite directions to balance each other.
If the scalar is > 1 the resultant vector will be larger and in the same direction. = 1 the resultant vector will be the same as the original vector. between 0 and 1 the resultant vector will be smaller and in the same direction. = 0 the resultant vector will be null. If the scalar is less than 0, then the pattern will be the same as above except that the direction of the resultant will be reversed.