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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} $

1 Answer

  • $\overrightarrow a\times\overrightarrow c$ 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.
answered Dec 7, 2013 by rvidyagovindarajan_1

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