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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) 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

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) 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

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Vectors In Two And Three Dimensions
Section9.4: Vectors In Three Dimensions
Problem 49E
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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)
Transcribed Image Text: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)
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
Transcribed Image Text: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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