Question

Find the cartesian equation of the following plane:
$straight r with rightwards arrow on top. space open parentheses straight i with hat on top space plus space straight j with hat on top space minus space straight k with hat on top close parentheses space equals space 2$

Solution

The equation of plane is $straight r with rightwards arrow on top. space open parentheses straight i with hat on top space plus space straight j with hat on top space minus space straight k with hat on top close parentheses space equals space 2$
or $open parentheses straight x space straight i with hat on top space plus space straight y space straight j with hat on top space plus space straight z space straight k with hat on top close parentheses. space open parentheses straight i with hat on top space plus space straight j with hat on top space minus space straight k with hat on top close parentheses space equals space 2 space space space space space space space space space space space space open square brackets because space stack straight r space with rightwards arrow on top space equals space straight x space straight i with hat on top space plus space straight y straight j with hat on top space plus space straight z space straight k with hat on top close square brackets$
or $left parenthesis straight x right parenthesis space left parenthesis 1 right parenthesis space space plus space left parenthesis straight y right parenthesis space left parenthesis 1 right parenthesis space plus space left parenthesis straight z right parenthesis thin space left parenthesis negative 1 right parenthesis space equals space 2$
or $straight x plus straight y minus straight z space equals space 2$
which is cartesian equation of plane.

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Three Dimensional Geometry

Find the cartesian equation of the following plane:
$straight r with rightwards arrow on top. space open parentheses straight i with hat on top space plus space straight j with hat on top space minus space straight k with hat on top close parentheses space equals space 2$

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