Q.The equation of the plane passing through (2, -1, 3) and making equal intercepts on the coordinate axes is
(A) x + y + z = 1
(B) x + y + z = 2
(C) x + y + z = 3
(D) x + y + z = 4

[!TLDR] Equal-intercept plane: $x+y+z=a$; substitute the given point to find $a$. …

A plane making equal intercepts $a,a,a$ on the coordinate axes has the intercept-form equation $\dfrac{x}{a}+\dfrac{y}{a}+\dfrac{z}{a}=1$, i.e. $x+y+z=a$.

Since the plane must pass through $(2,-1,3)$: …

Use the standard equal-intercept form $x+y+z=a$ (a plane with normal direction $(1,1,1)$), then substitute the given point's co …

Sign error adding $2+(-1)+3$; confusing "equal intercepts" with "equal in magnitude but of any sign," which is not what the standard form $x+y+z=a$ assumes (that for …