If the lines

$fraction numerator straight x minus 2 over denominator 1 end fraction space equals space fraction numerator straight y minus 3 over denominator 1 end fraction space equals space fraction numerator straight z minus 4 over denominator negative straight k end fraction and fraction numerator straight x minus 1 over denominator straight k end fraction space equals space fraction numerator straight y minus 4 over denominator 2 end fraction space equals space fraction numerator straight z minus 5 over denominator 1 end fraction$
are coplanar, then k can have

any value

exactly one value

exactly two values

exactly three values

Solution

exactly two values

open vertical bar table row 1 cell negative 1 end cell cell negative 1 end cell row 1 1 cell negative straight k end cell row straight k 2 1 end table close vertical bar space equals space 0 1 left parenthesis 1 plus 2 straight k right parenthesis space plus space 1 left parenthesis 1 plus straight k squared right parenthesis minus 1 left parenthesis 2 minus straight k right parenthesis space equals space 0 straight k squared space plus 1 plus 2 straight k space plus 1 minus 2 plus straight k space equals space 0 straight k squared plus 3 straight k space equals 0 left parenthesis straight k right parenthesis left parenthesis straight k plus 3 right parenthesis space equals 0 2 space values space of space straight k.

For Daily Free Study Material Join wiredfaculty