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Only question 4B please, so for question A i found that AB= (2, -4, -6)

and the obtuse angle is 120.61 degrees

so far for 4b i acknowledged that line l passes through both C and A so maybe i should use the direction vector of l?

an attempt of mine includes finding the magnitude of line AB then finding angle CAB, trigonometry but i had no idea how to obtain the Coordinate

please help, thanks

YEEEEEET Feb 4, 2019

#1**+5 **

Let coordinates of C be \(\begin{pmatrix} 4\\ 2\\ 9 \end{pmatrix} + \lambda \begin{pmatrix}-3\\-1\\2\end{pmatrix}\) as the line passes through C.

Rewrite the coordinates of C: \(\begin{pmatrix}4-3\lambda\\2-\lambda\\9+2\lambda\end{pmatrix}\).

The dot product of \(\vec{\text{BA}}\) and \(\vec{\text{BC}}\) is 0. (Why?)

\(\begin{pmatrix}-2\\4\\6\end{pmatrix} \begin{pmatrix}-2-3\lambda&&4-\lambda&&6+2\lambda\end{pmatrix} = 0\\ -2(-2-3\lambda) + 4(4-\lambda) + 6(6+2\lambda) = 0\\ 4 + 6\lambda + 16 - 4\lambda + 36 + 12 \lambda = 0\\ 14\lambda +56 = 0\\ \lambda = -4\)

So the coordinates of C is \(\begin{pmatrix}16\\6\\1\end{pmatrix}\).

MaxWong Feb 7, 2019