The vectors A_vec and B_vec have lengths A and B, respectively, and B_vec makes
ID: 1890160 • Letter: T
Question
The vectors A_vec and B_vec have lengths A and B, respectively, and B_vec makes an angle theta from the direction of A_vec.Vector addition using geometry
Vector addition using geometry is accomplished by putting the tail of one vector (in this case B_vec) on the tip of the other (A_vec) (Figure 1) and using the laws of plane geometry to find the length C, and angle phi, of the resultant (or sum) vector, ec{C}= ec{A}+ ec{B}:
C=sqrt{A^2 +B^2 -2 A B cos(c)},
phi = sin^{-1}left( rac{Bsin(c)}{C} ight).
Vector addition using components
Vector addition using components requires the choice of a coordinate system. In this problem, the x axis is chosen along the direction of A_vec (Figure 2) . Then the x and y components of B_vec are Bcos( heta) and Bsin( heta) respectively. This means that the x and y components of C are given by
C_x = A + Bcos( heta),
C_y = Bsin( heta).
Part A
Which of the following sets of conditions, if true, would show that the expressions 1 and 2 above define the same vector C_vec as expressions 3 and 4?
Check all that apply.
Check all that apply.
The two pairs of expressions give the same length and direction for C_vec.
The two pairs of expressions give the same length and x component for C_vec.
The two pairs of expressions give the same direction and x component for C_vec.
The two pairs of expressions give the same length and y component for C_vec.
The two pairs of expressions give the same direction and y component for C_vec.
The two pairs of expressions give the same x and y components for C_vec.
Explanation / Answer
Answer is:
The two pairs of expressions give the same length and direction for C_vec.
The two pairs of expressions give the same direction and x component for C_vec.
The two pairs of expressions give the same direction and y component for C_vec.
The two pairs of expressions give the same x and y components for C_vec.
Basically all of them except B and D.
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