Posted by Jake on Sunday, April 8, 2012 at 3:34am.
Which plane goes through the origin and is perpendicular to the line r=(2,2,1) + s(2,3,4), seR?
a) 2x2y+z=0
b) 2x+3y4z=0
c) 2x+3y+z4=0
d) none of the above.
I got D, none of the above. I have substituted and couldn't find the answer equal to zero.

Calculus  Reiny, Sunday, April 8, 2012 at 7:55am
1.
The line has direction numbers (2,3,4)
The direction numbers of the normal of plane b)
are (2,3, 4)
Since the normal is perpendicular to the plane
the given line is perpendicular to the plane
2.
Does (0,0,0 satisfy the equation of plane b) ?
LS = 2(0) + 3(0)  4(0) = 0
RS = 0 , so YES, it does
your correct answer is b)
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