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  • The plane, passing through the points (0, -1, 2) and (-1, 2, 1) and parallel to the line passing through (5,1,-7) and (1,-1,-1), also passes through the pointOpt

The plane, passing through the points (0, -1, 2) and (-1, 2, 1) and parallel to the line passing through (5,1,-7) and (1,-1,-1), also passes through the point

Option: 1

(0, 5, -2)


Option: 2

(-2, 5, 0)


Option: 3

(2, 0, 1)


Option: 4

(1, -2, 1)


Answers (1)

best_answer

Plane passing through (0,-1,0) and (-1,2,1)
Then vector in plane \langle-1,3,-1\rangle vector parallel to plane is \langle 4,2,-6\rangle
$$ \begin{aligned} & \text { Normal vector to plane }(\overrightarrow{\mathrm{n}})=\left|\begin{array}{ccc} \hat{\mathrm{i}} & \hat{\mathrm{j}} & \hat{\mathrm{k}} \\ -1 & 3 & -1 \\ 4 & 2 & -6 \end{array}\right| \\ & =\hat{\mathrm{i}}(16)-\hat{\mathrm{j}}(10)+\hat{\mathrm{k}}(-14) \\ & \overrightarrow{\mathrm{n}}=\langle 8,5,7\rangle \end{aligned}
Equation of plane
$$ \begin{aligned} & 8(x-0)+5(y+1)+7(z-2)=0 \\ & \Rightarrow 8 x+5 y+7 z=9 \end{aligned}
From given options point (-2,5,0) lies on plane.

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Anam Khan

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