Respuesta :
Answer:
50 units
Explanation:
Given,
- magnitude of the first vector = a = 30 units
- magnitude of the second vector = 70 units
As we know, From the law of vector addition,
Resultant of the addition of the two vectors is,
[tex]\therefor R\ =\ \sqrt{a^2\ +\ b^2\ +\ 2abcos\theta}[/tex]
where [tex]\theta[/tex] is the angle between the two vectors
And the value of [tex]cos\theat[/tex] lies between -1 ≤ [tex]cos\theta[/tex] ≥ 1.
For the possible values of the addition of the vectors
Therefore maximum possible value for the addition of the vector gives at the value of [tex]cos\theta\ =\ 1[/tex]
[tex]\therefore R_{max}\ =\ \sqrt{30^2\ +\ 70^2\ + 2\times 30\times 70\times 1}\\\Rightarrow R_{max}\ =\ 100 units[/tex]
Minimum possible value for the addition of the vectors gives at the value of [tex]cos\theta\ =\ -1[/tex]
[tex]\therefore R_{min}\ =\ \sqrt{30^2\ +\ 70^2\ + 2\times 30\times 70\times (-1)}\\\Rightarrow R_{min}\ =\ 40 units[/tex]
Hence the possible results of the addition of these two vectors is only 50 units which lies between the 40 units and 100 units.
