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\ {rac{a x_{1}+b y_{1}+c z_{1}+d}{a x_{2}+b y_{2}+c z_{2}+d}=0} \;\;\;\;\;\;\;\;\;\;\;\; {	ext { (same side) }} \\ {rac{a x_{1}+b y_{1}+c z_{1}+d}{a x_{2}+b y_{2}+c z_{2}+d}=\infty} \;\;\;\;\;\;\;\;\;\;\;{	ext { (opposite side) }}

In that case, one of the points lies in the plane if the value is zero then quotient point is in the plane and vice versa
# Engineering
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As we learned,   Direction Cosines - If are the angles which a vector makes with positive X-axis,Y-axis and Z-axis respectively then are known as diresction cosines, generally denoted by (l,m,n). - wherein       Substitute (i) in (ii)   and   m=-n                                                                                                  m=-2n l+5n-3n=0                         ...
# Engineering
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As we learnt in  Shortest distance between two skew lines (Cartesian form) - Shortest distance between and is given by Where    -    Normal vector of line is Put z=0 We get x+y=3 2x+3y=4 y=-2, x=5 (5,-2,0) is the point Equation of line will be Equation of z-axis is Shortest distance = Option 1) 1 This is incorrect option Option 2) 2 This is correct option Option 3) 3 This is...
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