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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)
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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 will happen if all components of a vector are reversed in direction?
Then the resultant vector is reversed.
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.
What is the angle between two vectors if their sum is to be maximum?
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 of addition how do you draw in the resultant vector?
When drawing a vector using the triangle method you will draw in the resultant vector using Pythagorean theorem. This is taught in physics.
How do you find the magnitude of the resultant vector?
To find the magnitude of the resultant vector, you can use the Pythagorean theorem. Simply square the x-component, square the y-component, add them together, and then take the square root of the sum. This will give you the magnitude of the resultant vector.
When are magnitudes of 2 vectors added?
The magnitudes of two vectors are added when calculating the resultant magnitude of their vector sum. This can be done using the Pythagorean theorem, where the magnitude of the resultant vector is the square root of the sum of the squares of the magnitudes of the individual vectors.
How do you calculate a vector sum?
To calculate a vector sum, add the corresponding components of the vectors together. This means adding the x-components to get the resultant x-component, and adding the y-components to get the resultant y-component. The magnitude of the resultant vector can be found using the Pythagorean theorem, and the direction can be determined using trigonometry.
Is cos function and pythagorean theroem used to calculate the magnitude and direction of the resultant vector?
Yes, the cosine function and Pythagorean theorem are often used to calculate the magnitude and direction of the resultant vector in a two-dimensional vector addition problem. The cosine function is used to determine the direction of the resultant vector, while the Pythagorean theorem is used to calculate its magnitude.
What is the equation for resultant velocity?
The equation for resultant velocity is the vector sum of the individual velocities. It can be calculated using the Pythagorean theorem in two dimensions, or by combining the x and y components of velocity using vector addition. Mathematically, it is represented as: v(resultant) = sqrt[(v1)^2 + (v2)^2 + 2v1v2cos(theta)]
What must you do to non-perpendicular vectors before you can use the Pythagorean theorem to calculate the resultant of the vectors?
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.
How do you find resultant velocity with perpendicular velocities?
To find the resultant velocity from two perpendicular velocities, you can use the Pythagorean theorem. Square each velocity, sum the squares, and then take the square root of the total to find the magnitude of the resultant velocity. The direction of the resultant velocity can be determined using trigonometry, typically with the arctangent function.
Formula to calculate magnitude of the resultant vector?
Magnitude of the resultant vector = Square root of[ (sum of x-components of all component vectors)2 plus(sum of y-components of all component vectors)2plus (sum of z-components of all component vectors)2 ]
How do you calculate the size of the resultant force in physics?
To calculate the size of the resultant force in physics, you can use vector addition. This involves determining the sum of the individual forces acting on an object, taking into account their magnitude and direction. The magnitude of the resultant force can be calculated using the Pythagorean theorem for forces acting at right angles, or vector addition for forces acting at angles other than 90 degrees.
What number is the length of a vector?
The length of a vector is a scalar quantity, typically denoted as a positive real number, that represents the magnitude or size of the vector. It is calculated using the vector's components in a coordinate system, often with the Pythagorean theorem.
When adding two vectors at right angles is the resultant of the vectors the algebraic sum of the two vectors?
No. Vectors add at rightangle bythe pythagoran theorem: resultant sum = square root of (vector 1 squared + vector 2 squared)
