Three Dimensional Geometry

Find the cartesian equation of the following plane: - Wired Faculty

Question

Find the cartesian equation of the following plane:
$straight r with rightwards arrow on top. space open square brackets left parenthesis straight s minus 2 space straight t right parenthesis space straight i with hat on top space plus space left parenthesis 3 minus straight t right parenthesis space straight j with hat on top space plus space left parenthesis 2 straight s plus straight t right parenthesis space straight k with hat on top close square brackets space equals space 15$

Solution

The equation of plane is

straight r with rightwards arrow on top. space open square brackets left parenthesis straight s minus 2 straight t right parenthesis space straight i with hat on top space plus space left parenthesis 3 minus straight t right parenthesis space straight j with hat on top space plus space left parenthesis 2 straight s plus straight t right parenthesis space straight k with hat on top close square brackets space equals space 15

open parentheses straight x space straight i with hat on top space space plus space straight y space straight j with hat on top space plus space straight z space straight k with hat on top close parentheses. space space space open square brackets left parenthesis straight s minus 2 space straight t right parenthesis space straight i with hat on top space plus space left parenthesis 3 minus straight t right parenthesis straight j with hat on top space plus space left parenthesis 2 straight s plus straight t right parenthesis space straight k with hat on top close square brackets space equals space 15

left parenthesis straight s minus 2 space straight t right parenthesis space straight x space space plus space left parenthesis 3 minus straight t right parenthesis space straight y space plus space left parenthesis 2 straight s plus straight t right parenthesis space straight z space equals space 15