If the plane 3x - 2y - z - 18 = 0 meets the c | vedclass

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(D) The given equation of the plane is $3x - 2y - z = 18$. Dividing by $18$ to convert it into intercept form $\frac{x}{a} + \frac{y}{b} + \frac{z}{c}

Vedclass · Accepted Answer

$(2, -3, -6)$

Vedclass · Answer

(D) The given equation of the plane is $3x - 2y - z = 18$. Dividing by $18$ to convert it into intercept form $\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1$: $\frac{3x}{18} - \frac{2y}{18} - \frac{z}{18} = 1$ $\frac{x}{6} + \frac{y}{-9} + \frac{z}{-18} = 1$. Thus,the plane meets the coordinate axes at points $A(6, 0, 0)$,$B(0, -9, 0)$,and $C(0, 0, -18)$. The centroid $(G)$ of $	riangle ABC$ with vertices $(x_1, y_1, z_1)$,$(x_2, y_2, z_2)$,and $(x_3, y_3, z_3)$ is given by $(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}, \frac{z_1+z_2+z_3}{3})$. $G = (\frac{6+0+0}{3}, \frac{0-9+0}{3}, \frac{0+0-18}{3}) = (2, -3, -6)$.

If the plane $3x - 2y - z - 18 = 0$ meets the coordinate axes at $A$,$B$,and $C$,then the centroid of $\triangle ABC$ is:

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