If they are parallel, you can add them algebraically to get a resultant vector. Then you can resolve the resultant vector to obtain the vector components.
Just by adding
Graphical Vector AdditionDraw your first vector. Then draw the tail (start) of your second vector at the tip (end) of your first vector. Then draw the tail of your third vector at the tip of you third vector (if it exists,) and so on. To find the resultant, draw a vector from the tail of the first vector to the tip of the last vector. The angle of the resultant will be between the resultant's tail and the first vector's tail. To find these values, it is recommended that you use a scale (e.g. 1cm:1m) and a protractor so that your values are accurate.Or, to do it mathematically (with 2 vectors):You have vector a with angle Ao, and vector b with angle Bo.To get vector c (resultant,) break the vectors up into their x and y components, then add the x and y components to find the x and y of the resultant. To find the magnitude of vector c, use Pythagoras's theorem, a2 + b2 = c2. To find the angle of c, use inverse tangent, tan-1(y/x)Example:Remember that sin = y and cos = x. Thus, to find the x component of a vector, use cos, and to find the y component of a vector, use sin.c = square root( (acosA + bcosB)2 + (asinA + bsinB)2 )angle of c = tan-1( (asinA + bsinB)/(bcosA + bcosB) )
If you assume the vector is only in two dimensions, you can find the missing y-component with Pythagoras' Theorem: y = square root of (magnitude2 - x2).
resultant
If they are parallel, you can add them algebraically to get a resultant vector. Then you can resolve the resultant vector to obtain the vector components.
To find the location of the resultant, you can use the parallelogram rule or the triangle rule of vector addition. Locate the endpoints of the vectors you are adding, draw the resultant vector connecting the initial point of the first vector to the terminal point of the last vector, and then find the coordinates of the endpoint 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 you combine 2 velocities that are in the same directions, add them together to find the resultant velocity. When you combine 2 velocities that are in opposite directions, subtract the smaller velocity from the larger velocity to find the resultant velocity.
Just by adding
the head to tail rule
The graphical method involves using vector diagrams to visually represent the vectors and their resultant. The analytical method involves breaking down the vectors into their components and then summing the components to find the resultant. The trigonometric method uses trigonometric functions to calculate the magnitude and direction of the resultant vector.
You can use the graphical method, which involves drawing vectors on a coordinate system and adding them tip-to-tail to find the resultant vector. Alternatively, you can use the component method, breaking each vector into its horizontal and vertical components and adding them separately to find the resultant vector.
Graphical Vector AdditionDraw your first vector. Then draw the tail (start) of your second vector at the tip (end) of your first vector. Then draw the tail of your third vector at the tip of you third vector (if it exists,) and so on. To find the resultant, draw a vector from the tail of the first vector to the tip of the last vector. The angle of the resultant will be between the resultant's tail and the first vector's tail. To find these values, it is recommended that you use a scale (e.g. 1cm:1m) and a protractor so that your values are accurate.Or, to do it mathematically (with 2 vectors):You have vector a with angle Ao, and vector b with angle Bo.To get vector c (resultant,) break the vectors up into their x and y components, then add the x and y components to find the x and y of the resultant. To find the magnitude of vector c, use Pythagoras's theorem, a2 + b2 = c2. To find the angle of c, use inverse tangent, tan-1(y/x)Example:Remember that sin = y and cos = x. Thus, to find the x component of a vector, use cos, and to find the y component of a vector, use sin.c = square root( (acosA + bcosB)2 + (asinA + bsinB)2 )angle of c = tan-1( (asinA + bsinB)/(bcosA + bcosB) )
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.
To find the resultant of the two vectors, break each vector into its horizontal and vertical components. Then add these components separately to find the total horizontal and vertical components. Finally, use these components to calculate the magnitude and direction of the resultant vector using trigonometry.
If you assume the vector is only in two dimensions, you can find the missing y-component with Pythagoras' Theorem: y = square root of (magnitude2 - x2).