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Question

(D) plane parallel to the $X$-axis has the general equation $by + cz + d = 0$. Since the plane passes through the points $(2, 3, 1)$ and $(4, -5, 3)$,

Vedclass · Accepted Answer

$y + 4z = 7$

Vedclass · Answer

(D) plane parallel to the $X$-axis has the general equation $by + cz + d = 0$. Since the plane passes through the points $(2, 3, 1)$ and $(4, -5, 3)$,these points must satisfy the equation. For point $(2, 3, 1)$: $b(3) + c(1) + d = 0 \implies 3b + c + d = 0$. For point $(4, -5, 3)$: $b(-5) + c(3) + d = 0 \implies -5b + 3c + d = 0$. Subtracting the two equations: $(3b + c + d) - (-5b + 3c + d) = 0 \implies 8b - 2c = 0 \implies c = 4b$. Substituting $c = 4b$ into the first equation: $3b + 4b + d = 0 \implies d = -7b$. The equation becomes $by + (4b)z - 7b = 0$. Dividing by $b$ (assuming $b 
eq 0$),we get $y + 4z = 7$. Thus,the correct option is $(D)$.

The equation of the plane passing through the points $(2, 3, 1)$ and $(4, -5, 3)$ and parallel to the $X$-axis is:

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