# 線性代數，投影求交點

find the point of intersection with the plane whose equation is x - 3y + 2z = 4

[x y z] = [1 -2 3] + t[2 5 -1]

### 1 Answer

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- 螞蟻雄兵Lv 71 decade agoFavorite Answer
find the point of intersection with the

plane whose equation is x－3y + 2z = 4

[x y z] = [1 －2 3] + t[2 5 －1]

Sol

[x y z] = [1 －2 3] + t[2 5 －1]=[2t+1 5t－2 －t+3]

ｘ－3y+2z=4

(2t+1)－3(5t－2)+2(－t+3)=4

2t+1－15t+6－2t+6=4

－15t+13=4

15t=9

t=3/5

(x，y，z)=(2*3/5+1，5*3/5－2，－3/5+3)=(11/5，1，12/5)

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