Browse Questions

# The number of vectors $\overrightarrow b$ of unit length which are $\perp$ to $\overrightarrow a=\hat i+2\hat j\:\:and\:\:\overrightarrow c=\hat j+2\hat k$ is?

$\begin{array}{1 1} 1 \\ 2 \\ 4 \\ Infinite\;vectors \end{array}$

Toolbox:
• $\overrightarrow a\times\overrightarrow c$ id $\perp$ to both $\overrightarrow a\:\:and\:\:\overrightarrow c$
Let $\overrightarrow b=x\hat i+y\hat j+z\hat k$
Given $\overrightarrow b$ is $\perp$ to both $\overrightarrow a\:\:and\:\:\overrightarrow c$ and $|\overrightarrow b|=1$
Since $\overrightarrow a\times\overrightarrow c\:\:and\:\:\overrightarrow c\times\overrightarrow a$ both vectors are $\perp$ to both $\overrightarrow a\:and\:\overrightarrow c$,
T\two such unit vectors are possible.