Question

If vector 1 have magnitude 5 unit.resultant of vector 1 and vector 2 have magnitude 15. which of the following value is a possible value of magnitude of vector 2

Answer 1

Answer:

Resultant maximum magnitude =10+5=15 units & minimum magnitude =10−5=5 units

Thus Resultant cannot be equal to 4 units.

Answer 2

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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