Browse Questions

# The number of vectors of unit length perpendicular to the vectors $\overrightarrow{a}=2\hat i+\hat j+2\hat k$ and $\overrightarrow{b}=\hat j+\hat k$ is

$(A)\;one\quad(B)\;two\quad(C)\;three\quad(D)\;infinite$

Toolbox:
• $\overrightarrow a \times \overrightarrow b=|\overrightarrow a| |\overrightarrow b| \sin \theta\; \hat n$
Let $\overrightarrow{a}=2\hat i+\hat j+2\hat k$ and $\overrightarrow{b}=\hat j+\hat k$
$\overrightarrow a \times \overrightarrow b=|\overrightarrow a| |\overrightarrow b| \sin \theta\; (\pm\hat n)$
Where $\hat n$ is the unit vector
This unit vector can be perpendicular either in the positive direction or negative direction
Hence the number of unit vector which are perpendicular to $\overrightarrow a$ and $\overrightarrow b$ is two
Hence the correct option is $B$