Equation Of Plane

Question

The equation of plane passing through (1, 2, 3) and perpendicular to line with direction ratios 2, 3, 4 is

RankGuru · Accepted Answer

1. **Identify Normal**: A plane perpendicular to a line has the line's direction ratios as its normal vector. Here, $\vec{n} = (2, 3, 4)$.
2. **Point-Normal Form**: Use the formula $A(x-x_1) + B(y-y_1) + C(z-z_1) = 0$.
3. **Substitution**: Substitute point $(1, 2, 3)$ and normal coefficients:
   $2(x-1) + 3(y-2) + 4(z-3) = 0$
4. **Simplification**:
   $2x - 2 + 3y - 6 + 4z - 12 = 0 \implies 2x + 3y + 4z - 20 = 0$
   $	herefore 2x + 3y + 4z = 20$.

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