Unit vector orthogonal to plane

olivia333
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Homework Statement



Find a unit vector with positive first coordinate that is orthogonal to the plane through the points P = (-4, 5, 4), Q = (-1, 8, 7), and R = (-1, 8, 8).

Homework Equations



u = PQ = Q - P
v = PR = R - P
ans = uXv = PQ X PR

The Attempt at a Solution



so I did:
PQ = Q - P = (3,3,3)
PR = R - P = (3,3,4)

Then I computed the cross product to get the answer.

|i..j..k|
|3 3 3| = <(12-9) , -(12-9) , (9-9)> = <3, -3, 0>
|3 3 4|

The 0 is correct but the 3 and -3 are not. What am I doing wrong?
Thanks!
 
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welcome to pf!

hi olivia! welcome to pf! :smile:
olivia333 said:
The 0 is correct but the 3 and -3 are not. What am I doing wrong?

not a unit vector? :wink:
 
ohhhh haha thank you so much!
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

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