Consider a Δ A B C where A 1 , 3 , 2 , B − 2 , 8 , 0 and C 3 , 6 , 7 . If the angle bisector of ∠ B A C meets the line B C at D , then the length of the projection of the vector A D → on the vector A C → is:

Step-by-step solution

Given, A 1 , 3 , 2 , B - 2 , 8 , 0 & C 3 , 6 , 7 And angle bisector of ∠ B A C meets the line B C at D , Now, plotting the diagram we get, Now, finding A C → = 2 i ^ + 3 j ^ + 5 k ^ ⇒ A C → = 4 + 9 + 25 = 38 And A B → = 9 + 25 + 4 = 38 Using angle bisector theorem, we get B D C D = A B A C ⇒ B D : C D = 1 : 1 Using section formula to find coordinates of D , ⇒ D ≡ 1 × 3 + 1 - 2 1 + 2 , 1 × 6 + 1 × 8 1 + 2 , 1 × 7 + 1 × 0 1 + 2 ⇒ D ≡ 1 2 , 7 , 7 2 ⇒ A D → = − 1 2 i ^ + 4 j ^ + 3 2 k ^ ⇒ A D → = 1 2 - i ^ + 8 j ^ + 3