# Find the vector and cartesian equations of the line passing through the point (2, 1, 3) and perpendicular to the lines (x-1)/1=(y-2)/2=(z-3)/3 and x/(-3)=y/2=z/5 - Mathematics

Find the vector and cartesian equations of the line passing through the point (2, 1, 3) and perpendicular to the lines

(x-1)/1=(y-2)/2=(z-3)/3 and x/(-3)=y/2=z/5

#### Solution

Let the D.R’s of the required line be a,b , c

therefore a+2b+3c=0 and -3a+2b+5c=0

=>a/4=b/(-14)=c/8

therefore DRS are 2,-7,4

Equations of line are (x-2)/2=(y-1)/(-7)=(z-3)/4

which is in vector form is,  vecr=(2hati+hatj+3hatk)+lambda(2hati-7hati+4hatk)

Concept: Equation of a Line in Space
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