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Line and Plane — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsLine and Plane3 Marks
Question
Find the vector equation of the plane passing through the point having position vector

$\hat{i}+\hat{j}+\hat{k}$ and perpendicular to the vector $4 \hat{i}+5 \hat{j}+6 \hat{k}$.

✓

Answer

The vector equation of the plane passing through the point $A(\bar{a})$ and perpendicular to the

vector $\bar{n}$ is $\bar{r} \cdot \bar{n}=\bar{a} \cdot \bar{n}$

Here, $\bar{a}=\hat{i}+\hat{j}+\hat{k}_1 \bar{n}=4 \hat{i}+5 \hat{j}+6 \hat{k}$

$\therefore \bar{a} \cdot \bar{n}=(\hat{i}+\hat{j}+\hat{k}) \cdot(4 \hat{i}+5 \hat{j}+6 \hat{k})$

= (1)(4) + (1)(5) + (1)(6) = 4 + 5 + 6 = 15

$\therefore$ the vector equation of the required plane is $\bar{r} \cdot(4 \hat{i}+5 \hat{j}+6 \hat{k})=15$.

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