Determine the magnitude of the vector sum V=V1 + V2 and the angle θx which V makes with the positive x-axis. Complete both graphical and algebraic solutions. Solve this question By Addition of vector by Rectangular component method?

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Determine the magnitude of the vector sum V=V1 + V2 and the angle θx which V makes with the positive x-axis. Complete both graphical and algebraic solutions. Solve this question By Addition of vector by Rectangular component method?


To add the vectors \vec v_1 and \vec v_2 you simply add the x and y components of each. If \vec v_1 = a \hat i+ b \hat j and \vec v_2 = c \hat i + d \hat j then \vec v_1 + \vec v_2 = (a+c) \hat i + (b+d) \hat j. Here \hat i and \hat j represent unit vectors in the x and y directions, respectively.

The angle that a vector \vec v = a\hat i + b \hat j makes to the horizontal axis can be found using \theta = arctan(\frac b a ).