Find the vector equation of the plane passing through (1, 2, 3) and perpendicular to the plane

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Solution

The position vector of the point (1, 2, 3) is

The direction ratios of the normal to the plane, , are 1, 2, and −5 and the normal vector is

The equation of a line passing through a point and perpendicular to the given plane is given by,

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Similar questions

(1, 2, 3)

\to r \cdot (^i + 2^j - 5^k) + 9 = 0

(1, 2, 3)

\to r . (^i + 2^j - 5^k) + 9 = 0

Find the vector equation of the straight line passing through (1, 2, 3) and perpendicular to the plane $r . (^i + 2^j - 5^k) + 9 = 0$

\vec{r} \cdot (\hat{i} + 2 \hat{j} - 5 \hat{k}) + 9 = 0 .

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