First slide

Planes in 3D

Question

The angle between the planes $2 x + y + z = 3,$ $x - y + 2 z = 5$ is

Moderate

A

$\frac{π}{2}$
B

$\frac{π}{6}$
C

$\frac{3 π}{4}$
D

$\frac{π}{3}$

Solution

$\cos θ = \frac{|(2) (1) + (1) (- 1) + (1) (2)|}{\sqrt{4 + 1 + 1} \sqrt{1 + 1 + 4}} = \frac{3}{6} = \frac{1}{2}$
$\Rightarrow θ = \frac{π}{3}$

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