Answer:
Option B is correct
Step-by-step explanation:
Given: [tex]\left | p \right |=7\sqrt{2}\,,\,\left | p+q \right |=12\sqrt{3}[/tex]
To find: interval on which [tex]\left | q \right |[/tex] must fall
Solution:
[tex]\left | p \right |=7\sqrt{2}\\-7\sqrt{2}\leq p\leq 7\sqrt{2}\,\,(i)[/tex]
[tex]\left | p+q \right |=12\sqrt{3}\\-12\sqrt{3}\leq p+q\leq 12\sqrt{3}\,\,(ii)[/tex]
Subtract (ii) from (i)
[tex]-12\sqrt{3}+7\sqrt{2}\leq p+q-p\leq 12\sqrt{3}-7\sqrt{2}\\-12\sqrt{3}+7\sqrt{2}\leq q\leq 12\sqrt{3}-7\sqrt{2}\\\left | q \right |=12\sqrt{3}-7\sqrt{2}[/tex]
So, [tex]\left | q \right |[/tex] must fall in interval [tex][12\sqrt{3}-7\sqrt{2},\infty)[/tex]
Therefore, option B is correct.
