Find a vector of magnitude 10 units and parallel to the resultant of t

1.	Find a vector of magnitude 10 units and parallel to the resultant of the vectors p = 3i -5j +7k and vector q =2i +5j -5k.
Answer» 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 \(\vec n=\frac{\pm10(-10\hat i+29\hat i+25\hat k)}{1-10\hat i+29\hat j+25\hat k }\) \(=\frac{\pm10(-10\hat i+29\hat j+25\hat k)}{\sqrt{(-10)^2+(29)^2+(25)^2}}\) \(=\frac{\pm10}{\sqrt{1566}}(-10\hat i+29\hat j+25\hat k)\)

Find a vector of magnitude 10 units and parallel to the resultant of the vectors p = 3i -5j +7k and vector q =2i +5j -5k.

Answer»

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

\(\vec n=\frac{\pm10(-10\hat i+29\hat i+25\hat k)}{1-10\hat i+29\hat j+25\hat k }\)

\(=\frac{\pm10(-10\hat i+29\hat j+25\hat k)}{\sqrt{(-10)^2+(29)^2+(25)^2}}\)

\(=\frac{\pm10}{\sqrt{1566}}(-10\hat i+29\hat j+25\hat k)\)

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Find a vector of magnitude 10 units and parallel to the resultant of the vectors p = 3i -5j +7k and vector q =2i +5j -5k.

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