Problema 3
\(\vec{A}=4i-3j+k\)\(=>Ax=\ 4,\ Ay=-3\ \) \(\ Az=1\)
\(\vec{V}=-i+j+4k\)\(=>Bx=-1,\ By=1\) \(Bz=4\)
\(\vec{A\ .\ \vec{B}}=\left(4\right)\left(-1\right)+\left(-3\right)\left(1\right)+\left(1\right)\left(4\right)\)
\(=-4-3+4=-3\)
\(COS\ \theta=\frac{\vec{A}.\vec{B}}{\left|\vec{A}\right|\left|\vec{B}\right|}=\frac{-3}{\left(\sqrt{26}\right)\left(\sqrt{18}\right)}=\frac{-3}{\sqrt{468}}=COS\theta^{-1}\left(\frac{-3}{\sqrt{468}}\right)=\theta=97.97\)
\(\left|\vec{A}\right|=\sqrt{Ax+Ay^2+Az^2}\) = \(\left|\vec{A}\right|\sqrt{\left(4\right)^2+\left(-3\right)^2+\left(1\right)^2}\) \(=\sqrt{16+9+1}\) \(=\sqrt{26}\) \(=5.09\)
\(\left|\vec{B}\right|\sqrt{Bx^2+By^2+Bz^2}\) \(=\left|\vec{B}\right|\sqrt{\left(-1\right)^2+\left(1\right)^2+\left(4\right)^2}\) \(=\sqrt{1+1+16}\) \(\sqrt{18\ }\) \(=4.24\)
\(\vec{Ax\vec{B}}=i\left[\left(-3\right)\left(4\right)-\left(1\right)\left(1\right)\right]-j\left[\left(4\right)\left(4\right)-\left(1\right)\left(-1\right)\right]\)\(+k\left[\left(4\right)\left(1\right)-\left(-3\right)\left(-1\right)\right]\)=
\(i\left[12-1\right]-j\left[16+1\right]+k\left[4-3\right]=\)
\(11i-17j+k\)
Problema 1
\(ay=A\sin\theta=7.3sen250=-6.85\)
\(ax=A\cos\theta=7.3\cos250=-2.49\)
Problema 2
\(=\sqrt{ax^2+ay^2}=\sqrt{\left(-25\right)^2+\left(40\right)^{2\ }}\)=\(\sqrt{625+1600}\)
\(\sqrt{2225}\)\(=47.16\)
\(Tan\theta=\frac{Ay}{Ax}=\theta\tan^{-1}\left(\frac{40}{-25}\right)=-57.99\)°