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A vector A and B make angle at 20 degree and 120 degree with x-axis . The magnitude of these vector s are 5m and 12 m respectively. Find the resultant vector?
Most Upvoted Answer
A vector A and B make angle at 20 degree and 120 degree with x-axis . ...
ResulTant Vector = Vector A + Vector B
= 5+12 = 17
= 5+12 = 17
Community Answer
A vector A and B make angle at 20 degree and 120 degree with x-axis . ...
Calculation of Resultant Vector
Given values:
- Angle between vector A and x-axis = 20°
- Angle between vector B and x-axis = 120°
- Magnitude of vector A = 5m
- Magnitude of vector B = 12m
Steps to Calculate Resultant Vector:
- Resolve vector A and vector B into their x and y components.
- Calculate the x and y components of the resultant vector using the formula:
- x-component of resultant vector = sum of x-components of vector A and vector B
- y-component of resultant vector = sum of y-components of vector A and vector B
- Calculate the magnitude of the resultant vector using the formula:
- magnitude of resultant vector = square root of [(x-component of resultant vector)^2 + (y-component of resultant vector)^2]
- Calculate the angle made by the resultant vector with the x-axis using the formula:
- angle made by resultant vector with x-axis = arctan(y-component of resultant vector / x-component of resultant vector)
Calculation:
- Components of vector A:
- x-component of vector A = 5 cos 20° = 4.75m
- y-component of vector A = 5 sin 20° = 1.71m
- Components of vector B:
- x-component of vector B = 12 cos 120° = -6m
- y-component of vector B = 12 sin 120° = 10.39m
- Components of resultant vector:
- x-component of resultant vector = 4.75m - 6m = -1.25m
- y-component of resultant vector = 1.71m + 10.39m = 12.1m
- Magnitude of resultant vector:
- magnitude of resultant vector = square root of [(-1.25m)^2 + (12.1m)^2] = 12.23m
- Angle made by resultant vector with x-axis:
- angle made by resultant vector with x-axis = arctan(12.1m / -1.25m) = -82.6°
Conclusion:
The resultant vector has a magnitude of 12.23m and makes an angle of -
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A vector A and B make angle at 20 degree and 120 degree with x-axis . The magnitude of these vector s are 5m and 12 m respectively. Find the resultant vector?
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A vector A and B make angle at 20 degree and 120 degree with x-axis . The magnitude of these vector s are 5m and 12 m respectively. Find the resultant vector? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A vector A and B make angle at 20 degree and 120 degree with x-axis . The magnitude of these vector s are 5m and 12 m respectively. Find the resultant vector? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vector A and B make angle at 20 degree and 120 degree with x-axis . The magnitude of these vector s are 5m and 12 m respectively. Find the resultant vector?.
A vector A and B make angle at 20 degree and 120 degree with x-axis . The magnitude of these vector s are 5m and 12 m respectively. Find the resultant vector? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A vector A and B make angle at 20 degree and 120 degree with x-axis . The magnitude of these vector s are 5m and 12 m respectively. Find the resultant vector? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vector A and B make angle at 20 degree and 120 degree with x-axis . The magnitude of these vector s are 5m and 12 m respectively. Find the resultant vector?.
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