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(B) The perpendicular distance $d$ from a point with position vector $c$ to the line $r = a + t\,b$ is given by the formula $d = \frac{|(c - a) 	imes

Vedclass · Accepted Answer

$|(c - a) 	imes b| \div |b|$

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(B) The perpendicular distance $d$ from a point with position vector $c$ to the line $r = a + t\,b$ is given by the formula $d = \frac{|(c - a) 	imes b|}{|b|}$.Let $P$ be any point on the line $r = a + t\,b$. The vector from the point $A$ (position vector $a$) to the point $C$ (position vector $c$) is $(c - a)$.The perpendicular distance $d$ is the magnitude of the component of the vector $(c - a)$ perpendicular to the vector $b$.This is given by the projection of $(c - a)$ onto the direction perpendicular to $b$,which is $\frac{|(c - a) 	imes b|}{|b|}$.

If the equation of a straight line passing through a point with position vector $a$ and parallel to the vector $b$ is $r = a + t\,b$,where $t$ is a parameter,then what is the perpendicular distance from this line to a point with position vector $c$?

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