Diketahui proyeksi vektor orthogonal p=xi - 2j + 4k pada q = 2i + 2j + k adalah r = 4i + 4 j + 2k. nilai x =....
anasyanura
![r= \frac{p.q}{|q|^2}.p\\ \left[\begin{array}{ccc}4\\4\\2\end{array}\right]= \frac{(x.2)+(-2.2)+(4.1)}{( \sqrt{4+4+1)^2} } \left[\begin{array}{ccc}2\\2\\1\end{array}\right] \\ \left[\begin{array}{ccc}4\\4\\2\end{array}\right] = \frac{2x}{9} \left[\begin{array}{ccc}2\\2\\1\end{array}\right] \\ 4= \frac{2x}{9}2 \\ \frac{4.9}{2}=2x\\ x=9](https://tex.z-dn.net/?f=r%3D+%5Cfrac%7Bp.q%7D%7B%7Cq%7C%5E2%7D.p%5C%5C%0A%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C4%5C%5C2%5Cend%7Barray%7D%5Cright%5D%3D+%5Cfrac%7B%28x.2%29%2B%28-2.2%29%2B%284.1%29%7D%7B%28+%5Csqrt%7B4%2B4%2B1%29%5E2%7D+%7D++%0A%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%5C%5C2%5C%5C1%5Cend%7Barray%7D%5Cright%5D+%5C%5C%0A%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C4%5C%5C2%5Cend%7Barray%7D%5Cright%5D+%3D++%5Cfrac%7B2x%7D%7B9%7D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%5C%5C2%5C%5C1%5Cend%7Barray%7D%5Cright%5D+%5C%5C%0A4%3D+%5Cfrac%7B2x%7D%7B9%7D2+%5C%5C%0A+%5Cfrac%7B4.9%7D%7B2%7D%3D2x%5C%5C%0Ax%3D9+++ "r= \frac{p.q}{|q|^2}.p\\ \left[\begin{array}{ccc}4\\4\\2\end{array}\right]= \frac{(x.2)+(-2.2)+(4.1)}{( \sqrt{4+4+1)^2} } \left[\begin{array}{ccc}2\\2\\1\end{array}\right] \\ \left[\begin{array}{ccc}4\\4\\2\end{array}\right] = \frac{2x}{9} \left[\begin{array}{ccc}2\\2\\1\end{array}\right] \\ 4= \frac{2x}{9}2 \\ \frac{4.9}{2}=2x\\ x=9")
1 votes
Thanks 4