The acute angle between the two lines whose direction ratios are connected by $$l+m$$−$$n=0$$ and $$l2+m2$$−$$n2=0$$ is

Question

The acute angle between the two lines whose direction ratios are connected by $$l+m$$−$$n=0$$  and  $$l2+m2$$−$$n2=0$$ is

Infinity Learn · Accepted Answer

Suppose that $$n=1Hence$$ the equations become $$l+m=1and$$ $$l2+m2=1Substitute$$ $$m=1$$−l in the equation  $$l2+m2=1and$$ then solve for lIt implies that $$l=1$$,$$0$$ and $$m=0$$,$$1Therefore$$, the direction ratios are $$1$$,$$0$$,$$1$$,$$0$$,$$1$$,$$1If$$ θ is the acute angle between two lines having direction ratios $$a1$$,$$b1$$,$$c1and$$ $$a2$$,$$b2$$,$$c2$$ then $$cos$$θ$$=a1a2+b1b2+c1c2a12+b12+c12$$⋅$$a22+b22+c22Suppose$$ that θ be the angle between the lines whose direction ratios are $$1$$,$$0$$,$$1$$,$$0$$,$$1$$,$$1Then$$ $$cos$$θ$$=122=12Therefore$$, the measure of angle θ is π$$3$$

The acute angle between the two lines whose direction ratios are connected by $l + m - n = 0 a n d l^{2} + m^{2} - n^{2} = 0$ is

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The acute angle between the two lines whose direction ratios are connected by l+m−n=0 and l2+m2−n2=0 is

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The acute angle between the two lines whose direction ratios are connected by $l + m - n = 0 a n d l^{2} + m^{2} - n^{2} = 0$ is