The direction ratios of two lines are given $$bya+b+c=0$$ and $$ab+bc$$−$$2ca=0$$ . Then the angle between the lines is

Question

The direction ratios of two lines are given $$bya+b+c=0$$ and $$ab+bc$$−$$2ca=0$$ . Then the angle between the lines is

Infinity Learn · Accepted Answer

Suppose that $$n=1Hence$$, the equations become $$a+b=1$$ and ab−$$b+2a=0Substitute$$ $$b=1$$−a in the equationab−$$b+2a=0$$  and then solve for aIt implies that $$l=2$$±$$3$$ and $$l=2$$±$$3Therefore$$, the direction ratios are $$2+3$$,−$$1$$−$$3$$,−$$1$$,$$2$$−$$3$$,−$$1+3$$,−$$1Suppose$$ that θbe the angle between the lines whose direction ratios are  $$2+3$$,−$$1$$−$$3$$,−$$1$$,$$2$$−$$3$$,−$$1+3$$,−$$1Hence$$, $$cos$$θ$$=4$$−$$3+1$$−$$3+12+32+$$−$$1$$−$$32+1$$⋅$$2$$−$$32+$$−$$1+32+1=0Therefore$$, the measure of angle θ is$$π$$$$2$$

The direction ratios of two lines are given by $a + b + c = 0 and a b + b c - 2 c a = 0$ . Then the angle between the lines is

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The direction ratios of two lines are given bya+b+c=0 and ab+bc−2ca=0 . Then the angle between the lines is

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The direction ratios of two lines are given by $a + b + c = 0 and a b + b c - 2 c a = 0$ . Then the angle between the lines is