Assignment ent Question 1 b.and C.each have a magnitude of 45.0 m and lie in an

Question

Assignment ent Question 1 b.and C.each have a magnitude of 45.0 m and lie in an xy plane. Their directions relative tothe positive direction of the x aas are 26.0 .. 192 e. Three vectors a , and 313 ., respectively. What are (a) the magritude and (b) the angle of the vector a + b + C (relative to the·x direction in the range of magnitude and (d) the angle of a Cin the range of (-180, 1800)? What are (e) the magnitude and () the angle (in the range of (-180°, 180) of a fourth vector d such that (a + b)-c d)-0 (a) Number (b) Number (c) Number (d) Number (e) Number (1) Number l ch Unit Unit Unit Unit Unit 3-50 PM

Explanation / Answer

a + b + c = ( 45) [( cos26 + cos192 + cos313)i + (sin26 + sin192 + sin313)j]

= 27.1 i - 22.5 j

(A) Magnitude = sqrt(27.1^2 + (-22.5)^2)

= 35.2 m

(B) theta = tan^-1(-22.5/27.1) = - 39.7 deg

  
a - b + c = (45) [( cos26 - cos192 + cos313)i + (sin26 - sin192 + sin313)j]

= 115.2 i - 3.83 j

(C) Magnitude = 115.3 m

(D) theta = 1.9 deg

(E) (a + b) - (c + d) = 0

45( (cos26 + cos192)i + (sin26 + sin192)j) - (45cos313i + 45 sin313 + D) = 0

(-3.57 i + 10.37 j) - (30.69i - 32.91 j + D) = 0

D = 34.26 i - 43.28j

Magnitude = 55.2 m

(F) theta = tan^-1(-43.28 / 34.26) = - 51.6 deg

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