If the equation of a line through a point a and parallel to vector b is \[\mathbf{r}=\mathbf{a}+t\,\mathbf{b},\] where t is a parameter, then its perpendicular distance from the point c is [MP PET 1998]

\[|(\mathbf{a}-\mathbf{b})\times \mathbf{c}|\div |\mathbf{c}|\]

\[|(\mathbf{c}-\mathbf{b})\times \mathbf{a}|\div |\mathbf{a}|\]

\[|(\mathbf{c}-\mathbf{a})\times \mathbf{b}|\div |\mathbf{b}|\]

\[|(\mathbf{a}-\mathbf{b})\times \mathbf{c}|\div |\mathbf{c}|\]

\[|(\mathbf{a}-\mathbf{b})\times \mathbf{c}|\div |\mathbf{a}+\mathbf{c}|\]

If the equation of a line through a point a and parallel to vector b i

1.	If the equation of a line through a point a and parallel to vector b is \[\mathbf{r}=\mathbf{a}+t\,\mathbf{b},\] where t is a parameter, then its perpendicular distance from the point c is [MP PET 1998]
A.	\[\|(\mathbf{c}-\mathbf{b})\times \mathbf{a}\|\div \|\mathbf{a}\|\]
B.	\[\|(\mathbf{c}-\mathbf{a})\times \mathbf{b}\|\div \|\mathbf{b}\|\]
C.	\[\|(\mathbf{a}-\mathbf{b})\times \mathbf{c}\|\div \|\mathbf{c}\|\]
D.	\[\|(\mathbf{a}-\mathbf{b})\times \mathbf{c}\|\div \|\mathbf{a}+\mathbf{c}\|\]
Answer» C. \[\|(\mathbf{a}-\mathbf{b})\times \mathbf{c}\|\div \|\mathbf{c}\|\]

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If the equation of a line through a point a and parallel to vector b is \[\mathbf{r}=\mathbf{a}+t\,\mathbf{b},\] where t is a parameter, then its perpendicular distance from the point c is [MP PET 1998]

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