Question

Vector problem

Answer 1

Can anyone help?

Answer 2

Question 14

Answer 3

I solved (a), I'm working on (b)

Answer 4

\(\vec{OA}=\vec{a}\\
\vec{OC}=\vec{c}\)

Then:
\( \vec{c}-\vec{a}=\vec{AC}\)
\( \vec{AC}+\vec{CD}=\vec{AD}, ~~\text{ or }~~(\vec{c}-\vec{a})+\vec{CD}=\vec{AD}\)

Now notice:
\(\vec{OC}=\vec{AB}=-\vec{BA}\)
\(\implies \vec{BA}=-\vec{OC}\)
And from your problem question: \(\vec{BD}=k\vec{BA}\)
Notice that \(\vec{BA}=k\vec{BA}+\vec{DA}
\\ \implies \vec{DA}=(1-k)\vec{BA}=(1-k)(-\vec{OC})=(1-k)(-\vec{c})\)

Now...
\( \vec{AC}+\vec{CD}=\vec{DA}\\
\implies(\vec{c}-\vec{a})+\vec{CD}=-(1-k)\vec{c}\)

then solve for \(\vec{CD}\)

Answer 5

Please refer to the diagram to make sure these equations make sense

Answer 6

unfortunately I gotta go. If you need help for later I can come back, or maybe someone else will come

Answer 7

thanks for your help