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l_1 = l_2 [br]\[br][br] \begin{bmatrix} 2\lambda \\ -2 \\ q - \lambda \end{bmatrix} = \begin{bmatrix} 8 + 2\mu \\ 3 + 5\mu \\ 5 + 4\mu \end{bmatrix}[br][br]\[br] [br] [br][br]so\ 2\lambda = 8+2\mu[br]\[br]-2 = 3 + 5\mu[br]\[br]q-\lambda = 5 + 4\mu[br]\[br]\Rightarrow \mu = -1 \Rightarrow \lambda = 3[br]\[br]q = 3 + 5 -4 = 4[br]\[br]P (6, -2, 1)
\begin{bmatrix} 2 \\ 0 \\ -1\end{bmatrix} \bullet \begin{bmatrix} 2 \\ 5 \\ 4 \end{bmatrix}[br]\[br]\Rightarrow 2(2) + 0(5) -1(4) = 0 \Rightarrow cos\theta = 0, \theta = 90\ \therefore\ perpendicular
9x^2 - 6xy + 4y^2 = 3[br]\[br]implicit\ differentiation[br]\[br]\18x - 6y -6x\dfrac{dy}{dx} + 8y\dfrac{dy}{dx} = 0[br]\[br]\Rightarrow \dfrac{dy}{dx} = \dfrac{6(3x-y)}{8y-6x}[br]\[br]\Stationary\ at \dfrac{dy}{dx} =0[br]\[br]3x-y = 0 \Rightarrow y = 3x[br]\[br]\Sub\ this\ into\ original\ equation[br]\[br]27x^2 = 3 \Rightarrow x = \dfrac{-1}{3}\ or \dfrac{1}{3} \Rightarrow y = 1\ or -1
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