Resultant vector \(\vec p\times\vec q\)\(=\begin{vmatrix}\hat i&\hat j&\hat k\\3&-5&7\\2&5&-5\end{vmatrix}\)
= \(\hat i(25-35)-\hat j(-15-14)+\hat k(15+10)\)
= -10\(\hat i\) + 29\(\hat j\) + 25\(\hat k\)
vector of magnitude 10 and parallel to resultant vector is
\(\vec n=\frac{\pm10(-10\hat i+29\hat i+25\hat k)}{1-10\hat i+29\hat j+25\hat k }\)
\(=\frac{\pm10(-10\hat i+29\hat j+25\hat k)}{\sqrt{(-10)^2+(29)^2+(25)^2}}\)
\(=\frac{\pm10}{\sqrt{1566}}(-10\hat i+29\hat j+25\hat k)\)
