Question

How do you find a unit vector that is orthogonal to both u = (1, 0, 1) v = (0, 1, 1)?

Answer 1

Answer:

one unit vector is ur=(-1/√3 ,1/√3 ,1/√3 )

Step-by-step explanation:

first we need to find a vector that is ortogonal to u and v . This vector r can be generated through the vectorial product of u and v , u X v :$r=u X v =\left[\begin{array}{ccc}i&j&k\\1&0&1\\0&1&1\end{array}\right] = \left[\begin{array}{ccc}0&1\\1&1\end{array}\right]*i + \left[\begin{array}{ccc}1&0\\1&1\end{array}\right]*j + \left[\begin{array}{ccc}1&0\\0&1\end{array}\right]*k = -1 * i + 1*j + 1*k = (-1,1,1)$

then the unit vector ur can be found through r and its modulus |r| :

ur=r/|r| = 1/[√[(-1)²+(1)²+(1)²]] * (-1,1,1)/√3 =(-1/√3 ,1/√3 ,1/√3 )

ur=(-1/√3 ,1/√3 ,1/√3 )