Find R=a+b for the vectors shown in Fig.1. Y R Z a a , X Vectors...

 

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Find R=a+b for the vectors shown in Fig.1. Y R Z a a , X Vectors a and b make angles a and B with the horizontal (x) axis. Take a=3, b=4, a=30, B=609 Method 1, geometry of triangles. Use the formula R = a + b + 2abcos(-a), noting that (B-a) is the angle external to the a,b,R triangle. Obtain R = ? Now use the sine law for the triangle to give sin/ b = sin(180 - (B-a)) / R to deduce A, the angle between R and a. Then deduce the angle + = R make with the x-axis. Method 2, the EASY way (and the way that easily extends to the multiple vector case!) Obtain the x- and y- components of both a and b and deduce the x- and y- components of R. Then deduce R = ? and the direction angle = ? Do you obtain the same answer for each method? Which method was quicker/easier? ? This is the angle that Find R=a+b for the vectors shown in Fig.1. Y R Z a a , X Vectors a and b make angles a and B with the horizontal (x) axis. Take a=3, b=4, a=30, B=609 Method 1, geometry of triangles. Use the formula R = a + b + 2abcos(-a), noting that (B-a) is the angle external to the a,b,R triangle. Obtain R = ? Now use the sine law for the triangle to give sin/ b = sin(180 - (B-a)) / R to deduce A, the angle between R and a. Then deduce the angle + = R make with the x-axis. Method 2, the EASY way (and the way that easily extends to the multiple vector case!) Obtain the x- and y- components of both a and b and deduce the x- and y- components of R. Then deduce R = ? and the direction angle = ? Do you obtain the same answer for each method? Which method was quicker/easier? ? This is the angle that