if vector 1 have magnitude 5 unit. resultant of vector 1 and vector 2 have magnitude 15. Which of the following value is possible value of magnitude of vector 2
Answers
Given : vector 1 have magnitude 5 unit.
resultant of vector 1 and vector 2 have magnitude 15
To Find : possible value of magnitude of vector 2
Solution:
vector 1 have magnitude = 5
magnitude of vector 2 = x
Let say α is the angle between vectors
Magnitude of resultant = √5² + x² - 2(5)xcosα
Magnitude of resultant = 15 unit
=> √5² + x² - 2(5)xcosα = 15
Squaring both sides
=> 25 + x² - 10xcosα = 225
=> x² - 10xcosα = 200
cosα range is [-1,1}
x² - 10x = 200 or x² + 10x = 200
x² - 10x = 200
=> (x - 20)(x + 10) = 0
=> x= 20 , - 10
x² + 10x = 200
=> (x + 20)(x - 10) = 0
=> x = - 20 or 10
possible value of magnitude of vector 2 is between 10 and 20 including both
10 ≤ x ≤ 20
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Answer:
vector 1 have magnitude e = 5
magnitude of vector 2 = x
Let say a is the angle between vectors
Magnitude of resultant 2(5)xcosa = √5² + x² -
Magnitude of resultant = 15 unit
=> √5² + x² - 2(5) a = 15
Squaring both sides
=> 25 + x² - 10cos a = 225
=> x² - cos a = 200
cosa range is [-1,1]
x ^ 2 - 10x = 200 or x ^ 2 + 10x = 200
x ^ 2 - 10x = 200
=> (x - 20)(x + 10) = 0
=> x= 20,- 10
x ^ 2 + 10x = 200
=> (x+20)(x - 10) = 0
=> x = 20 or 10
possible value of magnitude of vector 2 is between 10 and 20 including both,
10 ≤ x ≤ 20.