Question

The equation of plane passing through (1, 2,-1)
and containing the lines whose direction ratios
are 2, 1, 3 and 4, 1, 2

Answer 1

SOLUTION

TO DETERMINE

The equation of plane going through (1, 2,-1) and containing the lines whose direction ratios are 2, 1, 3 and 4, 1, 2

EVALUATION

Here it is given that the plane goes through the point (1, 2,-1)

Also the plane contains the the lines whose direction ratios are 2, 1, 3 and 4, 1, 2

Hence the required equation of the plane is

$\displaystyle \sf{\begin{vmatrix} \sf{x - 1} & \sf{y - 2} & \sf{z + 1}\\ \\ 2 & 1 & 3 \\ \\ 4 & 1 & 2 \end{vmatrix} = 0}$

$\displaystyle \sf{ \implies \: (x - 1)(2 - 3) - (y - 2)(4 - 12) + (z + 1)(2 - 4)= 0}$

$\displaystyle \sf{ \implies \: - (x - 1) + 8 (y - 2) - 2 (z + 1)= 0}$

$\displaystyle \sf{ \implies \: (x - 1) - 8 (y - 2) + 2 (z + 1)= 0}$

$\displaystyle \sf{ \implies \: x - 1 - 8 y + 16 + 2 z +2= 0}$

$\displaystyle \sf{ \implies \: x - 8 y + 2 z +17= 0}$

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