Question

The number of vectors of unit length perpendicular to vectors $\overline{a}=(1,1,0)$ & $\overline{b}=(0,1,1)$ is :

• A. $1$
• B. $2$
• C. $3$
• D. $\infty$

Answer 1

Answer: (B)

$2$

There exists two unit length vectors perpendicular to both of the vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ and it is given by $\frac{\overrightarrow{a}\times \overrightarrow{b}}{|\overrightarrow{a}\times \overrightarrow{b}|}$ and $\frac{\overrightarrow{b}\times \overrightarrow{a}}{|\overrightarrow{a}\times \overrightarrow{b}|}$.

So, the number of vector is $2$.