Question

Show
that
the
Equation 2x² - 6y- 12z² + 18yz+ 2zx+xy=o represent a
pair of planes. Also find the angle
between them​

Answer 1

Answer:

Answer:

Given : 2^{x} = 3{y} = 12^{z}

To show : (x+2y)z=xy

Let 2^{x} = 3^{y} = 12^{z} = k

2 = k^{1/x} 3 = k^{1/y) 12 = k^{1/z}

k^{1/z} = 12 = 2^{2}×3 = k{2/x}×k^{1/y}

k^{1/z} = k^{2/x+1/y}

\frac{2}{x} +\frac{1}{y} = \frac{1}{z}

x

2

+

y

1

=

z

1

Taking L.C.M and then cross multiplying

\frac{1}{z}= \frac{2y+x}{xy}

z

1

=

xy

2y+x

xy = (x+2y)z