Let $$L1$$ and $$L2$$ be the following straight line. $$L1$$:x−$$11=y$$−$$1=z$$−$$13$$ and $$L2$$:x−$$1$$−$$3=y$$−$$1=z$$−$$11Suppose$$ the straight lineL:x−α$$l=y$$−$$1m=Z$$−γ−$$2$$ lies in the plane containing $$L1$$ and $$L2$$ , and passes through the point of intersection of $$L1$$ and $$L2$$ . If the line L bisects the acute angle between the lines $$L1$$ and $$L2$$, then which of the following statements $$is/are$$ TRUE?

Question

Let $$L1$$ and $$L2$$ be the following straight line. $$L1$$:x−$$11=y$$−$$1=z$$−$$13$$ and $$L2$$:x−$$1$$−$$3=y$$−$$1=z$$−$$11Suppose$$ the straight lineL:x−α$$l=y$$−$$1m=Z$$−γ−$$2$$ lies in the plane containing $$L1$$ and $$L2$$ , and passes through the point of intersection of $$L1$$ and $$L2$$ . If  the line L bisects the acute angle between the lines $$L1$$ and $$L2$$, then which of the following  statements $$is/are$$ TRUE?

Infinity Learn · Accepted Answer

Point of intersection of $$L1$$&$$L2$$ is (1$$,$$0$$,$$1) Line L passes through (1$$,$$0$$,$$1)1$$−αℓ$$=$$−$$1m=1$$−γ−$$2----(1) acute angle bisector of $$L1$$&$$L2r$$→$$=i^+k^+$$λ$$i^$$−$$j^+3k^$$−$$3i^$$−$$j^+k^11r$$→$$=i^+k^+t(i^+j^$$−$$2k^)$$⇒ ℓ$$1=m1=$$−$$2$$−$$2$$⇒ℓ$$=m=1$$ From (1) $$1$$−α$$1=$$−$$1$$⇒α$$=2$$&$$1$$−γ−$$2=$$−$$1$$⇒γ$$=$$−$$1$$

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