(a)
The unit
(a)
Answer to Problem 3.17P
The unit vector perpendicular to the plane is
Explanation of Solution
Write an expression to calculate the unit vector perpendicular to the plane.
Here,
Write an expression to represent first vector.
Here,
Write an expression to represent first vector.
Here,
Write an expression to calculate the cross product of the vectors.
Write an expression to calculate the magnitude of the cross product of the vectors.
Here,
Conclusion:
Substitute
Substitute
Substitute
Thus, the unit vector perpendicular to the plane is
(b)
The unit vector perpendicular to the plane.
(b)
Answer to Problem 3.17P
The unit vector perpendicular to the plane is
Explanation of Solution
Write an expression to calculate the unit vector perpendicular to the plane.
Write an expression to calculate the cross product of the vectors.
Write an expression to calculate the magnitude of the cross product of the vectors.
Conclusion:
Substitute
Substitute
Substitute
Thus, the unit vector perpendicular to the plane is
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Chapter 3 Solutions
Vector Mechanics for Engineers: Statics
- F1 F2 ba C F3 A B d. b F4 Consider the following values: - F5 a = 7 m; b = 3 m; c = 7 m; d = 3 m; F1 = 3 kN; F2 = 11 kN; F3 = 2 kN; F4 = 20 kN; F5 = 2 kN; a = 30° e = 60° , B = 30° 1] What is the resultant moment of the five forces acting on the rod about point A? a) 90.8 kN.m b) 72.7 kN.m c) 14.6 kN.m d) 55.9 kN.m e) 21.6 kN.m f) 61.3 kN.m 2] What is the resultant moment of the five forces acting on the rod about point B? a) 77.8 kN.m b) 25.7 kN.m c) 38.6 kN.m d) 18.9 kN.m e) 37.9 kN.m f) 84.2 kN.m 3] What is the resultant moment of the five forces acting on the rod about point C? a) 35.7 kN.m b) 21.1 kN.m c) 714.6 kN.m d) 69.1 kN.m e) 51.4 kN.m f) 85.3 kN.m 4] What is the resultant moment of the five forces acting on the rod about point D? a) 17.8 kN.m b) 55.7 kN.m c) 44.6 kN.m d) 18.9 kN.m e) 21.5 kN.m f) 30.1 kN.m 5] What is the moment of the force F2 about point E? a) 81.7 kN.m b) 78.1 kN.m c) 64.6 kN.m d) 73.1 kN.m e) 54.6 kN.m f) 61.3 kN.marrow_forwardF1 F2 a F3 A B d b F4 Consider the following values: - F5 a = 12 m; b = 10 m; c = 10 m; d = 8 m; F1 = 6 kN; F2 = 7 kN; F3 = 8 kN; F4 = 9 kN; F5 = 10 kN; a = 30° , 0 = 45° , B = 60° 1] What is the resultant moment of the five forces acting on the rod about point A? a) - 111.6 kN.m b) 112.6 kN.m c) - 184.6 kN.m d) - 109.6 kN.m e) - 104.1 kN.m f) None of them 2] What is the resultant moment of the five forces acting on the rod about point B? a) -95.8 kN.m b) 42.7 kN.m c) 80.9 kN.m d) 10.9 kN.m e) 51.8 kN.m f) None of them 3] What is the resultant moment of the five forces acting on the rod about point C? a) 32.6 kN.m d) - 16.5 kN.m f) None of them b) - 21.1 kN.m c) 17.4 kN.m e) 15.6 kN.m 4] What is the resultant moment of the five forces acting on the rod about point D? a) 37.6 kN.m b) 73.8 kN.m c) 71.6 kN.m d) 52.1 kN.m e) 21.1 kN.m f) None of them 5] What is the moment of the force F2 about point E? a) 90.7 kN.m b) - 88.1 kN.m c) 54.6 kN.m d) 103.1 kN.m f) None of them e) 100.7 kN.m 6]…arrow_forwardIn Figure, find the magnitude of Qopa if you know that the resultant of the three forces is a vertical force, and it is equal to 620N downward. sol/ p=357.8N Q=240N To the left Q K 4 2 F=500Narrow_forward
- A ring is attached with 3 ropes. A force of P=250 lb is applied to the ring. The direction of the rope D is defined by 3 directions from each axis x, y and z: a = 80°, B = 45° and y = 30°. The direction of the rope C is defined by 2 directions from a plane and an axis: 0 70° and 8 = 20°. = X D B B d A 0 S What is the cartesian vector form of the tension Tp ?arrow_forwardF1 F2 a F3 A d b C F4 E Consider the following values: - F5 a = 12 m; b = 10 m; c = 10 m; d = 8 m; F1 = 6 kN; F2 = 7 kN; F3 = 8 kN; F4 = 9 kN; F5 = 10 kN; a = 30° , 0 = 45° ß = 60° 4] What is the resultant moment of the five forces acting on the rod ut point D? 51 What is the moment of the force F2 about point E? 6] What is the resultant moment of the five forces acting on the rod about point E?arrow_forwardF1 F2 a F3 A B d b F4 Consider the following values: - F5 a = 12 m; b = 10 m; c = 10 m; d = 8 m; F1 = 6 kN; F2 = 7 kN; F3 = 8 kN; F4 = 9 kN; F5 = 10 kN; a = 30°, 0 = 45° , B = 60° 4] What is the resultant moment of the five forces acting on the rod about point D? c) 71.6 kN.m f) None of them a) 37.6 kN.m b) 73.8 kN.m d) 52.1 kN.m e) 21.1 kN.m 5] What is the moment of the force F2 about point E? a) 90.7 kN.m b) - 88.1 kN.m c) 54.6 kN.m d) 103.1 kN.m e) 100.7 kN.m f) None of them 6] What is the resultant moment of the five forces acting on the rod about point E? a) 28.8 kN.m b) – 85.4 kN.m c) 111.6 kN.m d) 90,9 kN.m e) 85.4 kN.m f) None of themarrow_forward
- 2000Lbs 30° 60° y A' \ B The bar OA is fully constrained at O and attached to the cable AB. The bar length is 20', and it forms a 30° angle with the z-axis and its projection on the x– y plane forms a 60° angle with the x-axis. The point B is prescribed by the coordinates (8',16',0). If the force in the cable is 2000Lbs, what is the moment of this force about O? What is the moment of the 2000Lbs force about the axis OÁ.arrow_forwardGiven the Position vector R= 5i + 4j + 3k (m) and the Force vector F = 4i – 5j+3k (kN) Determine the angle in degrees between the two vectors. Answer:arrow_forwardF1 F2 a C F3 A d F4 D Consider the following values: - F5 a = 12 m; b = 10 m; c = 10 m; d = 8 m; F1 = 6 kN; F2 = 7 kN; F3 = 8 kN; F4 = 9 kN; F5 = 10 kN; a = 30° , e = 45° B = 60° 1] What is the resultant moment of the five forces acting on the rod about point A? a) - 111.6 kN.m b) 112.6 kN.m c) - 184.6 kN.m d) - 109.6 kN.m e) - 104.1 kN.m f) None of them 2] What is the resultant moment of the five forces acting on the rod about point B? a) -95.8 kN.m b) 42.7 kN.m c) 80.9 kN.m d) 10.9 kN.m e) 51.8 kN.m f) None of them 3] What is the resultant moment of the five forces acting on the rod about point C? a) 32.6 kN.m b) - 21.1 kN.m c) 17.4 kN.m d) - 16.5 kN.m e) 15.6 kN.m ) None of them 4] What is the resultant moment of the five forces acting on the rod about point D? a) 37.6 kN.m b) 73.8 kN.m c) 71.6 kN.m d) 52.1 kN.m e) 21.1 kN.m f) None of them 5] What is the moment of the force F2 about point E? a) 90.7 kN.m b) - 88.1 kN.m c) 54.6 kN.m d) 103.1 kN.m e) 100.7 kN.m f) None of them 6]…arrow_forward
- : 4i +k = 2i – 3j–k c= 2î + 3j- 2k d = -i+2j+k 1. a = Calculate the vector product a×b. Check that a xb is normal to a and to b. Calculate cxd and cx d. Find a unit vector normal to the plane of the vectors b and d.arrow_forwardF1 F2 a C F3 A F4 D Consider the following values: - F5 a = 16 m; b = 11 m; c = 13 m; d = 8 m; F1 = 3 kN; F2 = 11 kN; F3 a = 30°, 0 = 60° , B = 30° 2 kN; F4 = 20 kN; F5 = 2 kN; 1] What is the resultant moment of the five forces acting on the rod about point A? c) 19.6 kN.m a) 88.8 kN.m b) 76.3 kN.m d) 55.5 kN.m e) 59.1 kN.m f) 81.3 kN.m 2] What is the resultant moment of the five forces acting on the rod about point B? a) 88.8 kN.m b) 120.8 kN.m c) 31.6 kN.m d) 98.9 kN.m e) 41.1 kN.m ) 24.2 kN.m 3] What is the resultant moment of the five forces acting on the rod about point C? a) 125.7 kN.m b) 178.1 kN.m c) 254.6 kN.m d) 439.1 kN.m e) 144.1 kN.m ) 215.3 kN.m 4] What is the resultant moment of the five forces acting on the rod about point D? a) 77.8 kN.m b) 98.3 kN.m c) 100.6 kN.m d) 18.9 kN.m e) 97.1 kN.m ) 60.1 kN.m 5] What is the moment of the force F2 about point E? Activate W a) 122.7 kN.m b) 108.1 kN.m c) 66.6 kN.m d) 83.1 kN.m e) 111.1 kN.m ) 151.3 kN.m Go to Settingarrow_forwardQ1. Determine the moment, location and magnitude of the resultant about point G as shown in figure below. 35N 450 15 N G A 5 m 30 N 30⁰ F T 5 m E D 2.5 m 85 N 17 m 8 m с F1 60 N 60⁰ B 3.5 m 11 marrow_forward
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