A plane P meets the coordinate axes at A, B and C respectively. The centroid of $\Delta$ABC is given to be (1, 1, 2). Then the equation of the line through this centroid and perpendicular to the plane P is :
Solution
Let, Equation of plane is
<br><br>${x \over a} + {y \over b} + {z \over c}$ = 1
<br><br>A = ($a$, 0, 0) B
= (0, b, 0), C
= (0, 0, c)
<br><br>$\therefore$ Centroid = $\left( {{a \over 3},{b \over 3},{c \over 3}} \right)$ = (1, 1, 2)
<br><br>$\Rightarrow$ $a$ = 3, b = 3, c = 6
<br><br>$\therefore$ Plane : ${x \over 3} + {y \over 3} + {z \over 6}$ = 1
<br><br>$\Rightarrow$ 2x + 2y + z = 6
<br><br>The equation of the
line through this centroid (1, 1, 2) and <br>perpendicular to
the plane 2x + 2y + z = 6 is :
<br><br>${{x - 1} \over 2} = {{y - 1} \over 2} = {{z - 2} \over 1}$
About this question
Subject: Mathematics · Chapter: Three Dimensional Geometry · Topic: Direction Cosines and Ratios
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