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# ​ Vectors

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2 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

Feb 4, 2019

#1
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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 $$\begin{pmatrix}16\\6\\1\end{pmatrix}$$.

Feb 7, 2019
#2
+1

Ahh, because the dot product of perpendicular vectors are 0

i think the part i missed was to rewrite the coordinate of c

Thank you very much!

YEEEEEET  Feb 7, 2019
edited by YEEEEEET  Feb 7, 2019