Roy asked in 科學數學 · 8 years ago

數學 向量Vectors跟 Matrices

想請教這種入門題型該怎麼解呢?

1. A vector equation for a given straight line is r = (i + 3 j) + λ (−i − j).

(a) Show that the point (1, 2) does not lie on this line.

(b) Construct a vector equation for the line that does go through the point (1, 2), and is perpendicular to r.(c) Determine the pointof intersection of the two lines.

如題

還有一問, λ 這個符號代表的是什麼意思呢

Update:

λ=parameter(參數)........參數方程式

有白話一點的解釋嗎?

是某個向量的延伸嗎?

Update 2:

想請教(b)小題的解法如何去理解呢?

Update 3:

像是為什麼要除以-1

a跟b又是什麼關鍵...

1 Answer

Rating
  • 麻辣
    Lv 7
    8 years ago
    Favorite Answer

    想請教這種入門題型該怎麼解呢?1. A vector equation for a given straight line is r=(i+3j)+λ(−i−j).

    如題還有一問, 這個符號代表的是什麼意思呢?λλ=parameter(參數)........參數方程式(a) Show that the point (1, 2) does not lie on this line.r=(i+3j)+λ(−i−j)=(1-λ)i+(3-λ)j=P(1,2)=> 1-λ=1, & 3-λ=2λ=0, λ=1 兩者矛盾∴ P(1,2)不在r上

    (b) Construct a vector equation for the line that does go through the point (1, 2), and is perpendicular to r.r=(1-λ)i+(3-λ)j=> x=1-λ, y=3-λ(x-1)/(-1)=(y-3)/(-1)=λ...................a∴ Normal: (x-1)/1=(y-2)/(-1)=λ......b=> x=1+λ, y=2-λRn=(1+λ)i+(2-λ)j..........ans

    (c) Determine the pointof intersection of the two lines.

    Eq.a: -x+y=2Eq.b: x+y=3Add: y=5/2Sub: x=1/2Intersection=(1/2,5/2).............ans

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