The line x - 2 3 = y - 3 4 = z - 4 5 is parallel to the plane:

Question

The line $\frac{x - 2}{3} = \frac{y - 3}{4} = \frac{z - 4}{5}$ is parallel to the plane:

Smart Achievers · Accepted Answer

(3)

Ans. $2 x + y - 2 z = 0$

Explanation:

$D.R.:$ $3 \hat{i} + 4 \hat{j} + 5 \hat{k} = \vec{a}$ $(say)$

$\vec{a} \cdot \vec{n} = 0$

$∴$ $(3 \hat{i} + 4 \hat{j} + 5 \hat{k}) \cdot \vec{n} = 0$

$From option (3)$

$(3 \hat{i} + 4 \hat{j} + 5 \hat{k}) \cdot (2 \hat{i} + \hat{j} - 2 \hat{k})$ $= 3 (2) + 4 (1) + 5 (- 2)$

$= 0$

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