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(B) The equation of any plane passing through the intersection of the planes $P_1: x + 2y + 3z - 4 = 0$ and $P_2: 4x + 3y + 2z + 1 = 0$ is given by $P

Vedclass · Accepted Answer

$17x + 14y + 11z = 0$

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(B) The equation of any plane passing through the intersection of the planes $P_1: x + 2y + 3z - 4 = 0$ and $P_2: 4x + 3y + 2z + 1 = 0$ is given by $P_1 + \lambda P_2 = 0$. $(x + 2y + 3z - 4) + \lambda (4x + 3y + 2z + 1) = 0$. Since this plane passes through the origin $(0, 0, 0)$,we substitute $x=0, y=0, z=0$ into the equation: $(0 + 0 + 0 - 4) + \lambda (0 + 0 + 0 + 1) = 0$. $-4 + \lambda = 0 \implies \lambda = 4$. Substituting $\lambda = 4$ back into the equation: $(x + 2y + 3z - 4) + 4(4x + 3y + 2z + 1) = 0$. $x + 2y + 3z - 4 + 16x + 12y + 8z + 4 = 0$. $17x + 14y + 11z = 0$.

What is the equation of the plane passing through the intersection of the planes $x + 2y + 3z - 4 = 0$ and $4x + 3y + 2z + 1 = 0$,and also passing through the origin?

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