## Analytical Method of Vector Addition – Class 11 | Chapter – 4 | Physics Short Notes Series PDF for NEET & JEE

Analytical Method of Vector Addition: The analytical method of vector addition involves using the components of vectors to find the resultant vector. This method is particularly useful when dealing with vectors in two or three dimensions. The analytical method of vector addition is particularly useful when working with vectors that do not form right angles, or when working with vectors that cannot be easily drawn to scale. By using the components of vectors, we can easily add and subtract vectors in two or three dimensions, and obtain the magnitude and direction of the resultant vector using simple trigonometric formulas.

## Steps in Analytical Method of Vector Addition

Here are the steps involved in the analytical method of vector addition:

• Resolve each vector into its components along the x and y (or x, y, and z) axes using trigonometry. For example, if v is a vector with a magnitude of v and an angle θ with respect to the x-axis, then its x-component is given by vx = v cos θ, and its y-component is given by vy = v sin θ.
• Add the x-components of all the vectors to find the resultant x-component, and add the y-components of all the vectors to find the resultant y-component. If you are working in three dimensions, add the z-components as well.
• Use the Pythagorean theorem to find the magnitude of the resultant vector. For example, if the resultant vector has x- and y-components of rx and ry, respectively, then its magnitude, r, is given by r = √(rx2 + ry2). In three dimensions, the magnitude can be found using the formula r = √(rx2 + ry2 + rz2).
• Use trigonometry to find the direction of the resultant vector. For example, if the angle between the resultant vector and the x-axis is θr, then θr = tan-1(ry/rx).

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