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

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Solution

DRs of line perpendicular to plane is =(1 , 2 , -5)
line equation is $\frac{x - 1}{1} = \frac{y - 2}{2} = \frac{z - 3}{- 5}$

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

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

(1, 2, 3)

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

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

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

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