The plane passing through the point $$(-2$$, $$-2$$, $$2)$$ and containing the line joining the points (1$$, $$1$$, $$1) and (1$$, $$-1$$, $$2) makes intercepts on the coordinate axes, the sum of whose lengths is

Question

Infinity Learn · Accepted Answer

Equation of the  required plane is $$ax+2+by+2+cz$$−$$2=0d$$.r.'s  of the line passing through $$Ax1$$,$$y1$$,$$z1$$,$$Bx2$$,$$y2$$,$$z2$$ are $$x2-x1$$,$$y2-y1$$,$$z2-z1$$ ∴d.r.'s of the line are <$$0$$,$$2$$,$$-1$$>⇒$$2b-c=0$$ and $$3a+b=0$$ Put $$b=$$λ∴$$c=2$$λ;$$a=-$$λ$$3$$∴$$-$$λ$$3(x+2)+$$λ$$(y+2)+2$$λ$$(z-2)=0$$⇒−$$x+3y+6z$$−$$8=0$$⇒x−$$8+y83+z43=1$$∴sum of the lengths of the $$intercepts=8+83+43=12$$

The plane passing through the point (-2, -2, 2) and containing the line joining the points (1, 1, 1) and (1, -1, 2) makes intercepts on the coordinate axes, the sum of whose lengths is

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