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

Question
Asked Oct 28, 2019
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Learning Goal:
Review | Constants
To understand that adding vectors by using geometry
and by using components gives the same result, and
that manipulating vectors with components is much
easier.
The vectors A and B have lengths A and B, respectively, and B makes an angle 0 from the direction of
A.
Vectors may be manipulated either geometrically or
using components. In this problem we consider the
addition of two vectors using both of these two
methods
Vector addition using geometry
Vector addition using geometry is accomplished by putting the tail of one vector (in this case B) on the
tip of the other (A) (Figure 1) and using the laws of plane geometry to find the length C, and angle , of
Figure
1 of 2
the resultant (or sum) vector, C
A + B
A2B2-2AB cos(c),
1. C
(ga)
B sin(c)
2. sin
Vector addition using components
B
Vector addition using components requires the choice of a coordinate system. In this problem, the x axis
is chosen along the direction of A (Figure 2). Then the x and y components of B are B cos (0) and
B sin(0) respectively. This means that the x and y components of C are given by
A
3. Ca AB cos (0)
4. Cy Bsin(0)
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Learning Goal: Review | Constants To understand that adding vectors by using geometry and by using components gives the same result, and that manipulating vectors with components is much easier. The vectors A and B have lengths A and B, respectively, and B makes an angle 0 from the direction of A. Vectors may be manipulated either geometrically or using components. In this problem we consider the addition of two vectors using both of these two methods Vector addition using geometry Vector addition using geometry is accomplished by putting the tail of one vector (in this case B) on the tip of the other (A) (Figure 1) and using the laws of plane geometry to find the length C, and angle , of Figure 1 of 2 the resultant (or sum) vector, C A + B A2B2-2AB cos(c), 1. C (ga) B sin(c) 2. sin Vector addition using components B Vector addition using components requires the choice of a coordinate system. In this problem, the x axis is chosen along the direction of A (Figure 2). Then the x and y components of B are B cos (0) and B sin(0) respectively. This means that the x and y components of C are given by A 3. Ca AB cos (0) 4. Cy Bsin(0)

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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 as expressions 3 and 4?
Check all that apply
The 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 for
The 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 C
The 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 C
Submit
Request Answer
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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 as expressions 3 and 4? Check all that apply The 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 for The 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 C The 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 C Submit Request Answer

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Expert Answer

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

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and 6 15t th

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