Vectors...

[Ressha]

ABCD is a quadrilateral. T is the midpoint of BC. Given AB = i + 3j and AT = 3 / 2i + j where i and j are the unit vectors parallel to the x-axis and y-axis. Find the length of the CD.

I’M STUCK!!!

 

[Dr.Peterson]

It seems to me that D can be anywhere, so we don't have enough information to find CD.

Check that you copied the problem correctly! Did you omit a picture that gives additional information? It will be best if you can post an image of the original problem.

 

[Ressha]

 

[Dr.Peterson]

Do you not see that this is an erroneous problem? As I said, I can put D anywhere I like without changing the conditions of the problem:

There is some mistake in the statement of the problem; either a condition was omitted, or it is supposed to be a specific kind of quadrilateral, or there is a typo somewhere. I can tell you what AC is, but not AD or CD.

 

[pka]

We are given that \(\overrightarrow {AB} = i + 3j~\&~\overrightarrow {AT} = \frac{3}{2}i + j\).
So \(\overrightarrow {AB} + \overrightarrow {BT} = \overrightarrow {AT} \) or \( \overrightarrow {BT} = \overrightarrow {AT}-\overrightarrow {AB} \)
\(\overrightarrow {BT}=\overrightarrow {CT}\)
Therefore \(\overrightarrow {AC} = \overrightarrow {AT} + \overrightarrow {TC} \)

 

[Ressha]

We are given that \(\overrightarrow {AB} = i + 3j~\&~\overrightarrow {AT} = \frac{3}{2}i + j\).
So \(\overrightarrow {AB} + \overrightarrow {BT} = \overrightarrow {AT} \) or \( \overrightarrow {BT} = \overrightarrow {AT}-\overrightarrow {AB} \)
\(\overrightarrow {BT}=\overrightarrow {CT}\)
Therefore \(\overrightarrow {AC} = \overrightarrow {AT} + \overrightarrow {TC} \)

Got it.Thanks.

 

[Ressha]

Do you not see that this is an erroneous problem? As I said, I can put D anywhere I like without changing the conditions of the problem:
View attachment 19882
There is some mistake in the statement of the problem; either a condition was omitted, or it is supposed to be a specific kind of quadrilateral, or there is a typo somewhere. I can tell you what AC is, but not AD or CD.

I’m so sorry for the mistake in that question. I got it from my exercise book. Will try another question instead.Thank you.