Linear algebra -hyperplane question?!
Favorites|Homepage
Subscriptions | sitemap
HOME > > Linear algebra -hyperplane question?!

Linear algebra -hyperplane question?!

[From: ] [author: ] [Date: 12-06-22] [Hit: ]
0) and contains both the point P(a, a, a, a, a, a) an point Q(a,......
can someone explain to me how i can find the following:

Hyperplane H in R6 is perpendicular to the vector (1, -1, 2, 1, -1, 0) and contains both the point P(a, a, a, a, a, a) an point Q(a, -a, -a, a+2, 1, 3) for some specific value a

What is the value of a?

thank so much

-
If P and Q are on the hyperplane, then the vector QP is parallel to the plane.
QP = OP - OQ = (a, -a, -a, a+2, 1, 3) - (a, a, a, a, a, a) = (0, -2a, -2a, 2, 1-a, 3-a)

Since the vector (1, -1, 2, 1, -1, 0) is perpendicular to the plane, then

(1, -1, 2, 1, -1, 0) • (0, -2a, -2a, 2, 1-a, 3-a) = 0

2a - 4a + 2 -1 + a = 0

1 - a = 0

a = 1
1
keywords: algebra,Linear,hyperplane,question,Linear algebra -hyperplane question?!
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .