Here two vectors are given of lengths
[tex]\vec l_1 = 8 units[/tex]
[tex]\vec l_2 = 3 units[/tex]
now let say the two vectors are inclined at some angle with each other
so the resultant is given as
[tex]R = \sqrt{l_1^2 + l_2^2 + 2l_1 l_2 cos\theta}[/tex]
now plug in all values
[tex]R = \sqrt{8^2 + 3^2 + 2(8)(3)cos\theta}[/tex]
Now for maximum resultant the angle between two vectors must be ZERO degree
[tex]R_{max} = \sqrt{8^2 + 3^2 + 2(8)(3)} = 11 units[/tex]
Now for minimum resultant the angle between two vectors must be 180 degree
[tex]R_{max} = \sqrt{8^2 + 3^2 - 2(8)(3)} = 5 units[/tex]
