Solve Coplanar Vector Problem with a, b, and c Vectors | Find all Values of t

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Homework Statement


Find all values of t so that the three vectors a=(1,2,3) b=(4,5,6) and c=(7,8,t) are coplanar.

Homework Equations


(axb) \bullet c=0

The Attempt at a Solution



(1, 2, 3) x (4, 5, 6)
(-3,6,-3)
(-3,6,-3)\bullet(7,8,t)
27=3t
t=9

it says find ALL values of t. i keep getting 9 through different combinations. is there only one value of t? thnks
 
Last edited:
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Yes, there is only one value of t. If you'd gotten 27=0*t for your last equation then any t would work. But you didn't.
 

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...
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