# hw1sol - Physics 1A HW1 Solutions 1 Geometric vs...

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Physics 1A HW1 Solutions 1. Geometric vs Componentwise Vector Addition (a) The question is essentially asking which of the choices are suﬃcient to uniquely specify the vector ~ C . Knowing the magnitude and direction is suﬃcient for specifying ~ C . As is knowing the x and y components of ~ C . Knowing the direction θ and the x or y components, C x or C y , is also suﬃcient, since one can get the magnitude C = C x / sin θ , and we’d recover the ﬁrst case. Knowing only the length and x (or y ) component of ~ C is NOT suﬃcient, since there is still an ambiguity in the sign of the y (or x ) component. That is, given C and C x , then C y = a and C y = - a , where a is the true y component, both satisfy C = p C 2 x + C 2 y , or vice versa. (b) C = p C 2 x + C 2 y = p ( A + B cos θ ) 2 + ( B sin θ ) 2 = A 2 + B 2 + 2 AB cos θ (c) We need only the ﬁrst two conditions: A 2 + B 2 - 2 AB cos c = p A 2 + B 2 - 2 AB cos ( π - θ ) = A 2 + B 2 + 2 AB cos θ (d) With the x axis along ~ A , then geometry gives

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hw1sol - Physics 1A HW1 Solutions 1 Geometric vs...

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