# Learning Goal:Review | ConstantsTo understand that adding vectors by using geometryand by using components gives the same result, andthat manipulating vectors with components is mucheasier.The vectors A and B have lengths A and B, respectively, and B makes an angle 0 from the direction ofA.Vectors may be manipulated either geometrically orusing components. In this problem we consider theaddition of two vectors using both of these twomethodsVector addition using geometryVector addition using geometry is accomplished by putting the tail of one vector (in this case B) on thetip of the other (A) (Figure 1) and using the laws of plane geometry to find the length C, and angle , ofFigure1 of 2the resultant (or sum) vector, CA + BA2B2-2AB cos(c),1. C(ga)B sin(c)2. sinVector addition using componentsBVector addition using components requires the choice of a coordinate system. In this problem, the x axisis chosen along the direction of A (Figure 2). Then the x and y components of B are B cos (0) andB sin(0) respectively. This means that the x and y components of C are given byA3. Ca AB cos (0)4. Cy Bsin(0) Part AWhich of the following sets of conditions, if true, would show that the expressions 1 and 2 above definethe same vector C as expressions 3 and 4?Check all that applyThe two pairs of expressions give the same length and direction for C.C.The two pairs of expressions give the same length and x component forThe two pairs of expressions give the same direction and x component for C.The two pairs of expressions give the same length and y component for CThe two pairs of expressions give the same direction and y component for C.The two pairs of expressions give the same x and y components for CSubmitRequest Answer

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A vector is defined by length and direction. So both expressions must the same length and direction for vector C...

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