First slide

Planes in 3D

Question

If the plane $\frac{x}{2} + \frac{y}{3} + \frac{z}{6} = 1$ cuts the axes of coordinates at points A, B and C, then find the area of the triangle ABC.

Moderate

A

18 sq unit
B

36 sq unit
C

$3 \sqrt{14}$ sq unit
D

$2 \sqrt{14}$ sq unit

Solution

Plane meets axis at A(2,0, 0),8(0, 3, 0) and C(0, 0, 6). Then area of $∆$ ABC is
$\begin{array}{l} \frac{1}{2} | \vec{AB} \times \vec{AC} | \\ = \frac{1}{2} | (- 2 \hat{i} + 3 \hat{j}) \times (- 2 \hat{i} + 6 \hat{j}) | \\ = 3 \sqrt{14} sq units \end{array}$

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