First slide

Planes in 3D

Question

Equation of the plane passing through the points P (1,1,- 1), Q(3,0,2) and R (- 2, 1,0)?

Moderate

A

$(2 \hat{i} - 3 \hat{j} + 3 \hat{k}) \cdot ((x + 2) \hat{i} + (y - 1) \hat{j} + z \hat{k}) = 0$
B

$x = 3 - t, y = - 11 t, z = 2 - 3 t$
C

$(x + 2) + 11 (y - 1) = 3 z$
D

$(2 \hat{i} - \hat{j} + 3 \hat{k}) \times (- 3 \hat{i} + \hat{k}) \cdot ((x + 2) \hat{i} + (y - 1) \hat{j} + z \hat{k}) = 0$

Solution

${\vec{V}}_{1}, {\vec{V}}_{2}, \vec{P S}$ are in the same plane
$\begin{array}{ll} ∴ (2 \hat{i} - \hat{j} + 3 \hat{k}) \times (- 3 \hat{i} + \hat{k}) \cdot ((x + 2) \hat{i} + (y - 1) \hat{j} + z \hat{k}) = 0 \end{array}$

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