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

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Solution

Line passes through the point (1, 2, 3).
It is perpendicular to the given plane.
Hence, it is parallel to the normal vector of the plane.
Therefore, it is parallel to the line - $ˆ i + 2 ˆ j - 5 ˆ k$
Therefore, equation of the required line is :
$\to r$ = $(ˆ i + 2 ˆ j + 3 ˆ k)$ + $λ (ˆ i + 2 ˆ j - 5 ˆ k)$

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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

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

\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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