# Thread: parallelogram using vectors

1. ## parallelogram using vectors

given the four points:
A= (1,4,-2) B=(5,6,-2) C=(3,0,2) D=(7,2,2)

show that ABCD is a parallelogram using vectors.
is it a parallelogram? square? rhombus?

if I'm correct, in order for vectors to be parallel, they must be scalar multiples of one another. So i found the vectors of these points, but I got

vector AB= <4,2,-4>
vector BC=<-2,-6,4>
vector CD= <4,2,0>
vector AD= <-6,2,4>

not sure what I did wrong

2. Originally Posted by cottekr
given the four points:
A= (1,4,-2) B=(5,6,-2) C=(3,0,2) D=(7,2,2)

show that ABCD is a parallelogram using vectors.
is it a parallelogram? square? rhombus?

if I'm correct, in order for vectors to be parallel, they must be scalar multiples of one another. So i found the vectors of these points, but I got

vector AB= <4,2,-4> <4,2,0>
vector BC=<-2,-6,4>
vector CD= <4,2,0>
vector AD= <-6,2,4> <6,-2,4>
only two sides parallel ... sure you have the correct coordinates?

3. $\displaystyle \begin{array}{l} \overrightarrow {AB} = \left\langle {4,2,0} \right\rangle \\ \overrightarrow {BC} = \left\langle { - 2, - 6,4} \right\rangle \\ \overrightarrow {CD} = \left\langle {4,2,0} \right\rangle \\ \overrightarrow {DA} = \left\langle { - 6,2, - 4} \right\rangle \\ \end{array}$