Q27 of 43 Page 1

If the linesandare perpendicular, find the value of k and hence find the equation of the plane containing these lines.

Given equations are –


L1:


It can also be represented in vector form.


∴ L1:


And L2:


It can also be represented in vector form.


∴ L2:


For lines to be perpendicular, the dot product of their direction vectors must be zero.


∴


⇒ -3k – 2k + 10 = 0


⇒ -5k = -10


∴ k = 2


∴ equation of line can be rewritten as –


L1:


And L2:


Equation of plane containing the lines is given by -


= 0


⇒ (x – 1) (-20 – 2) – (y – 2) (-15 – 4) + (z – 3) (-3 + 8) = 0


⇒ -22x + 19y + 5z = 31


Required equation of the plane is: -22x + 19y + 5z = 31


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