let $x= (1,-2, 2), y=(3, 4, -2)$ be position vectors. $x,y$,origin form parallelogram with $4^{\text{th}}$ point $z$ lying opposite origin.

Question

For this question we need to find $z$. I found vector $XY$ as I thought that would give me position of z however that wasn't correct. I am unsure on what to do now.

Answer 1

From the parallelogram law of vector addition,

$$\vec{z} = \vec{x} + \vec{y}$$