Answer:
[tex]\hat{w}=\dfrac{\vec{5i+13j-k}}{13.92}[/tex]
Explanation:
It is given that,
[tex]\vec{u}=2i-j-3k[/tex]
[tex]\vec{v}=-3i+j-2k[/tex]
Taking the cross product of v and v such that,
[tex]\vec{w}=u\times v[/tex]
[tex]\vec{w}=(2i-j-3k)\times (-3i+j-2k)[/tex]
[tex]\vec{w}=5i+13j-k[/tex]
[tex]|w|=\sqrt{5^2+13^2(-1)^2}[/tex]
|w| = 13.92
Let [tex]\hat{w}[/tex] is the unit vector normal to the plane containing u and v. So,
[tex]\hat{w}=\dfrac{\vec{w}}{|w|}[/tex]
[tex]\hat{w}=\dfrac{\vec{5i+13j-k}}{13.92}[/tex]
Hence, this is the required solution.
