First slide

Planes in 3D

Question

Equation of the plane through the mid-point of the join of A(4,5,-10) and B(-1,2,1) and perpendicular to AB is

Moderate

A

$5 x + 3 y - 11 z + \frac{135}{2} = 0$
B

$5 x + 3 y - 11 z = \frac{135}{2}$
C

$5 x + 3 y + 11 z = 135$
D

$5 x + 3 y - 11 z + \frac{185}{2} = 0$

Solution

Mid point of AB = $(\frac{3}{2}, \frac{7}{2}, \frac{- 9}{2})$
D.r’s of AB are (5,3,-11)
Equation of plane is $[\bar{r} - (\frac{3}{2} \bar{i} + \frac{7}{2} \bar{j} - \frac{9}{2} \bar{k})] . (5 \bar{i} + 3 \bar{j} - 11 \bar{k}) = 0$
$\bar{r} . (5 \bar{i} + 3 \bar{j} - 11 \bar{k}) = \frac{135}{2}$

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