First slide

Planes in 3D

Question

The angle between the planes represented by $2 x^{2} - 6 y^{2} - 12 z^{2} + 18 y z + 2 z x + x y = 0$ is

Moderate

A

$C o s^{- 1} (\frac{16}{21})$
B

$C o s^{- 1} (\frac{17}{21})$
C

$C o s^{- 1} (\frac{19}{21})$
D

$\frac{π}{2}$

Solution

The equation $2 x^{2} - 6 y^{2} - 12 z^{2} + 18 y z + 2 z x + x y = 0$ represents two planes and they are
$2 x - 3 y + 6 z = 0 .......... (1)$
$x + 2 y - 2 z = 0 .......... (2)$
If $θ$ is the angle between the planes (1) and (2) then $\cos θ = \frac{| (2) (1) + (- 3) (2) + 6 (- 2) |}{\sqrt{2^{2} + {(- 3)}^{2} + 6^{2}} \sqrt{1^{2} + 2^{2} + 2^{2}}}$ $= \frac{16}{21}$
$∴ θ = C o s^{- 1} \frac{16}{21}$
Method 2:
$\cos θ = \frac{| a + b + c |}{\sqrt{{(a + b + c)}^{2} + 4 (f^{2} + g^{2} + h^{2} - a b - b c - c a)}}$
$\begin{array}{l} 8 + 4 k + 24 = 0 \\ k = - 8 \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App