Question

Determine whether the planes are parallel, perpendicular or neither. 2x â 4y + 3z = 5, x + 8y + 10z = 3

Answer 1

The given two planes 2x + 4y + 3z = 5 and x + 8y + 10z = 3 are perpendicular to each other.

According to the given question.

We have two planes

2x - 4y + 3z = 5

and,

x + 8y + 10z = 3

Since, two planes are perpenicular if

$a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2} = 0$

Where $a_{1}$, $b_{1}$ and $c_{1}$ and $a_{2}$, $b_{2}$ and $c_{2}$ are the direction ratios of planes.

And the two planes are parallel to each other if

$\frac{a_{1} }{a_{2} } =\frac{b_{1} }{b_{2} } = \frac{c_{1} }{c_{2} }$

Here, the direction ratios of plane 2x + 4y + 3z = 5 are 2, -4, and 3  and the direction ratios of plane x + 8y + 10z = 3 are 1, 8, and 10

Now,

2(1) + (-4)(8) + 3(10)

= 2 - 32 + 30

= 0

Since, the sum of the product of the direction ratios of  the two palnes is 0. Therefore, the given two planes 2x + 4y + 3z = 5 and x + 8y + 10z = 3 are perpendicular to each other.

Find out more information about perpendicular and parallel planes here:

brainly.com/question/19580509

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