A line with direction ratios $$2$$,$$1$$,$$2$$ intersect each of the lines $$x=y+a=z$$ and $$x+a=2y=2z$$ the $$co-ordinates$$ of each of the points of intersection are

Question

A line with direction ratios $$2$$,$$1$$,$$2$$ intersect each of the lines  $$x=y+a=z$$ and  $$x+a=2y=2z$$  the $$co-ordinates$$ of each of the points of intersection are

Infinity Learn · Accepted Answer

The given lines $$arex1=y+a1=z1$$,  $$x+a2=y1=z1Suppose$$ that the line L intersect the above two lines at P,QThe direction rations of PQ are $$2$$,$$1$$,$$2The$$ points   Ps,s−a,sand  $$Q2t$$−a,t,t, these are general points on the given two lines. Direction ratios of  PQare  $$2t$$−a−s,t−$$s+a$$,t−s, these are proportional to $$2$$,$$1$$,$$2It$$ implies that $$2t$$−a−$$s2=t$$−$$s+a1=t$$−$$s2Hence$$, $$s=3a$$,$$t=aTherefore$$, the points of intersections are   $$P3a$$,$$2a$$,$$3a$$, Qa,a,a

A line with direction ratios $〈2, 1, 2〉$ intersect each of the lines $x = y + a = z$ and $x + a = 2 y = 2 z$ the co-ordinates of each of the points of intersection are

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A line with direction ratios 2,1,2 intersect each of the lines x=y+a=z and x+a=2y=2z the co-ordinates of each of the points of intersection are

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A line with direction ratios $〈2, 1, 2〉$ intersect each of the lines $x = y + a = z$ and $x + a = 2 y = 2 z$ the co-ordinates of each of the points of intersection are