Grade 12 math: vector equation of a plane
Favorites|Homepage
Subscriptions | sitemap
HOME > Mathematics > Grade 12 math: vector equation of a plane

Grade 12 math: vector equation of a plane

[From: ] [author: ] [Date: 11-05-25] [Hit: ]
7) + s(0, 0, 1) + t(1, -2,i dont get which direction vectors you use........
Find the vector equation of the plane containing the point A(1, -2, 7) and the z-axis.

Answer: r = (1, -2, 7) + s(0, 0, 1) + t(1, -2, 6)

i don't get which direction vectors you use... I'm getting confused. Can someone help me?
51 minutes

-
Given the position vector xₒ of a point P and two directions d1 and d2, the vector equation of the plane through P containing d1 and d2 is r = xₒ + sd1 +td2, where s and t are scalars.

This comes from completing the triangle of vectors formed by P and any point r in the desired plane. The sides of the triangle are || to and scalar multiples of d1 and d2.

We can take P as (1,−2,7) and d1 = (0,0,1). For d2, take any point Q on the z-axis ( say (0,0,1) ) and let d2 = PQ = (1,−2, 6). This gives desired equation.

This is a bit contrived to give stated answer. Undirected, I would have taken origin (0,0,0) as P and d2 = PO = (1,−2,7) so plane would be r = u(0, 0, 1) + v(1, −2, 7). Putting u = s−t and v = t+1 gives quoted result but this is a simpler equation.
1
keywords: equation,plane,of,12,Grade,math,vector,Grade 12 math: vector equation of a plane
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .