Question

Vector Question

Answer 1

Question 14, thanks

Answer 2

Who can help?

Answer 3

a rhombus is a parallelogram (i.e. opposite sides are parallel) with all sides being the same length.

Answer 4

Given
\[ \vec{OA}=\vec{a}\\ \vec{OC}=\vec{c}\\\vec{BD} = k \vec{BA} \]
Using the fact we have a rhombus:
\[ \vec{CB}=\vec{OA}= \vec{a} \]
and for the same reason
\[ \vec{BA}= \vec{CO}= -\vec{OC}= -\vec{c}\]
and so (using this and the given):
\[ \vec{BD} = k \vec{BA} = -k\vec{c}\]

meanwhile, for point D we want to go from OC to CB to BD
\[D= \vec{c}+\vec{a}-k\vec{c}\]
and the vector we want is
\[ \vec{CD}= D-C=\vec{c}+\vec{a}-k\vec{c} - \vec{c} \\= \vec{a}-k\vec{c}\]

Answer 5

Wow, I understand now, but how can I find the value of k?

Answer 6

There are a few ways.

maybe the easiest is to use geometry