The Cartesian equation of the plane $\vec{r}\cdot(\hat{i}+\hat{j}-\hat{k}) = 2$ is-

(a) $x+y-z=0$
(b) $x+y-z=2$
(c) $x+y-z=1$
(d) $x+y+z+2=0$

Question

The Cartesian equation of the plane $\vec{r}\cdot(\hat{i}+\hat{j}-\hat{k}) = 2$ is-

(a) $x+y-z=0$
(b) $x+y-z=2$
(c) $x+y-z=1$
(d) $x+y+z+2=0$

Accepted Answer

> [!TLDR]
> Substitute $\vec r=x\hat i+y\hat j+z\hat k$ into the vector equation of the plane and take the dot product.
>
> Given $\vec r\cdot(\hat i+\hat j-\hat k)=2$, with $\vec r=x\hat i+y\hat j+z\hat k$:
> …

Q.The Cartesian equation of the plane $\vec{r}\cdot(\hat{i}+\hat{j}-\hat{k}) = 2$ is-

Concept understanding — Equation of a Plane

Equation of a Plane

Point + normal form

Normal (perpendicular) form

Intercept form …

Q.The Cartesian equation of the plane r⃗⋅(i^+j^−k^)=2\vec{r}\cdot(\hat{i}+\hat{j}-\hat{k}) = 2r⋅(i^+j^​−k^)=2 is-

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Q.The Cartesian equation of the plane $\vec{r}\cdot(\hat{i}+\hat{j}-\hat{k}) = 2$ is-

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