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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

Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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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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