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Question
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)`
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