Let P be the plane passing through (1,1,1) and parallel to the lines L 1 and L 2 having direction ratios 1,0,-1 and -1,1,0 respectively. If A,B and C are the points at which P intersects the coord

Question

Let P be the plane passing through (1,1,1) and parallel to the lines L 1 ​ and L 2 ​ having direction ratios 1,0,-1 and -1,1,0 respectively. If A,B and C are the points at which P intersects the coordinate axes find the volume of the tetrahedron whose vertices are A,B,C and the origin.

TestHub · Accepted Answer

The two line directions give the plane normal: $(1, 0, - 1) \times (- 1, 1, 0) = (1, 1, 1) .$ $x + y + z = 3.$

The plane passes through (1,1,1), so its constant is 3. Each axis intercept is 3.

$V = \frac{3 \cdot 3 \cdot 3}{6} = \frac{9}{2} = 4.5.$

Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

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