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A plane passes through three points A, B and C with position vectors , and respectively. The…
A plane passes through three points A, B and C with position vectors $\hat{i} + \hat{j}$, $\hat{j} + \hat{k}$ and $\hat{k} + \hat{i}$ respectively. The equation of the line passing through the point P with position vector $\hat{i} + 2\hat{j} + 2\hat{k}$ and normal to the plane is (Application)
- (a)$\vec{r} = (\hat{i} + 2\hat{j} + 2\hat{k}) + \lambda(\hat{i} + \hat{j} + \hat{k}),\ \lambda \in \mathbb{R}$
- (b)$\vec{r} = (\hat{i} + \hat{j} + \hat{k}) + \lambda(\hat{i} + 2\hat{j} + 2\hat{k}),\ \lambda \in \mathbb{R}$
- (c)$\vec{r} \cdot (\hat{i} - \hat{j} - \hat{k}) = \hat{i} + 2\hat{j} + 2\hat{k}$
- (d)$x - 1 = y = z$
Answer
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From ISC 2026 Specimen Mathematics Paper 1, question 15(ii).
Check your working with the 3D geometry and vectors calculator: points, vectors, lines and planes: distances, angles, foot and image, shortest distance, intersections.