and are unit vectors along x- and y- axis respectively. What is the magnitude and direction of the vectors, and ? What are the components of a vector along the directions of and? [You may use graphical method]


Any vector quantity in x-y plane is represented as linear combination of two unit vectors one along x direction and other along y direction namely and , coefficient of and represent magnitude of vector quantity in x and y direction respectively


for any vector


of px and py represent magnitude of vector quantity in x and y direction respectively


the magnitude is given by



And angle with x axis is given by



Here let the vectors be


and


Now considering


X component ax = 1 unit


Y component ay = 1 unit


So magnitude of vector is



Or


Now for direction angle with x axis



Or


So angle made with x axis is


Now considering


X component bx = 1 unit


Y component by = -1 unit


So magnitude of vector is



Or


Now for direction angle with x axis



Or


So angle made with x axis is


As shown Graphically in the figure



Now component of one vector in the direction of other vector is the magnitude of vector in direction of other


Now let us say we have to find component of in the direction of let us angle between them is

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