56 VectorsQ3.10Any vector that points along a line at 45° to the xand yaxes has components equal in magnitude.Q3.11ABxx=and AByy=.Q3.12Addition of a vector to a scalar is not defined. Think of apples and oranges.Q3.13One difficulty arises in determining the individual components. The relationships between a vectorand its components such as AAx=cosθ,are based on right-triangle trigonometry. Another problemwould be in determining the magnitude or the direction of a vector from its components. Again,AAAxy=+22only holds true if the two component vectors, Axand Ay, are perpendicular.Q3.14If the direction of a vector is specified by giving the angle of the vector measured clockwise from thepositive y-axis, then the x-component of the vector is equal to the sine of the angle multiplied by themagnitude of the vector.SOLUTIONS TO PROBLEMSSection 3.1Coordinate SystemsP3.1xr==°=
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