Question

Juno

想問這題

A
D
++
N
-邊長為1的正方形ABCD, DN =
2
3
CD、BM = - BC,求M.成 =-
5
AN
B
M

Answer 1

✨ 最佳解答 ✨

qn

AM = AB + ⅗BC = AB + ⅗AD
AN = AD + ½DC = AD + ½AB

AM · AN = (AB + ⅗AD) · (½AB + AD)
= ½|AB|² + ⅗|AD|² + (13/10)(AB·AD)

AB ⟂ AD ⇒ AB · AD = 0

AM · AN = ½|AB|² + ⅗|AD|² = 1/2 + 3/5 = 11/10

qn

或是座標化
AM = (1, ⅗)
AN = (½, 1)
⇒ AM · AN = ½ + ⅗ = 11/10

Juno

懂了！感謝感謝❤️