Simple Hyperplane Equation - What am I Missing?

[cowmoo32]

I'm trying to learn linear algebra using Schaum's outline and this is one of the practice problems:

Find and equation of the hyperplane H in R⁴ that passes through P(3,-4,1,-2) and is normal to u=[2,5,-6,-3]

The equation is in the form 2_x1+5_x2-6_x3-3_x4 = k

They say to substitute P into the equation to obtain k=-26 but I keep coming up with k=-14. This is simple math but I'm clearly missing something. Where am I going wrong?

 

[micromass]

It's probably a typo.

 

[Mythic]

Let X be a point in the hyperplane. Then u.(X-P)=0 should be your equation.

So, 2(x1 - 3) + 5(x2 + 4) - 6(x3 - 1) - 3(x4 + 2) = 0

2x1 + 5x2 - 6x3 - 3x4 + 14 = 0

Same answer you get. Is there a typo somewhere?

 

[cowmoo32]

There has to be a typo because the next problem is similar and the answer there is correct.