Two Vectors Three Here are two vectors: a = (6.0 m) i - (2.0 m) j and b =(3.0 m)

Question

Two Vectors Three Here are two vectors:
a = (6.0 m)i - (2.0 m)j and b =(3.0 m)i +(5.0 m)j. (a) What is the magnitude ofa?
m
(b) What is the angle of a(relative toi)?
? °

(c) What is the magnitude of b?
? m
(d) What is the angle of b?
?°

(e) What is the magnitude of a +b?
? m
(f) What is the angle of a +b?
?°

(g) What is the magnitude of b -a?
? m
(h) What is the angle of b -a?
?°

(i) What is the magnitude of a -b?
? m
(j) What is the angle of a -b?
?°

a = (6.0 m)i - (2.0 m)j and b =(3.0 m)i +(5.0 m)j. (a) What is the magnitude ofa?
m
(b) What is the angle of a(relative toi)?
? °

(c) What is the magnitude of b?
? m
(d) What is the angle of b?
?°

(e) What is the magnitude of a +b?
? m
(f) What is the angle of a +b?
?°

(g) What is the magnitude of b -a?
? m
(h) What is the angle of b -a?
?°

(i) What is the magnitude of a -b?
? m
(j) What is the angle of a -b?
?°

(a) What is the magnitude ofa?
m
(b) What is the angle of a(relative toi)?
? °

(c) What is the magnitude of b?
? m
(d) What is the angle of b?
?°

(e) What is the magnitude of a +b?
? m
(f) What is the angle of a +b?
?°

(g) What is the magnitude of b -a?
? m
(h) What is the angle of b -a?
?°

(i) What is the magnitude of a -b?
? m
(j) What is the angle of a -b?
?°

Explanation / Answer

a = (6.0m)i - (2.0m)j and b = (3.0 m)i + (5.0 m)j (a). magnitude of vector a = [ 6 ^ 2 + ( -2 ) ^ 2] = 6.32 m (b).required angle = tan -1 ( -2 / 6 )                               = -18.43 degree                               = 360 - 18.43 = 341.56 degrees (c). Magnitude of vectro b = [ 3^2 + 5 ^ 2 ] =5.83 m (d). angle = tan -1 ( 5/ 3 )                    =59.03 degrees (e). a+b = ( 6 + 3 ) i + ( -2 + 5 ) j             = 9i + 3j magnitude = [ 9 ^ 2 + 3 ^ 2 ] = 9.4868 m (f). angle = tan -1 ( 3 / 9 ) = 18.43 degrees (g ) b - a = ( 3-6 ) i + ( 5 + 2 ) j               = -3i + 7 j magnituide = [ -3^ 2 + 7 ^ 2 ]                  = 7.615 m angle = tan -1 ( 7 / 3 )         = -66.8degrees     Since it is in 2 ndquadratant         = 180 - 66.8 =113.19 degrees

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