Show that the following planes are at right angle: `x-2y+4z=10\ a n d\ 18 x+17 y+4z=49.`

Explanation

Here , Given planes, `x-2 y+4 z=10 and 18 x+17 y+4 z=49`

It is known that planes `a_{1} x+b_{1} y+c_{1} z+d_{1}=0` and `a_{2} x+b_{2} y+c_{2} z+d_{2}=0` are at right angles

if, `a_{1} a_{2}+b_{1} b_{2}+c_{1} c_{2}=0 ldots ldots (a)`

We have, `a_{1}=1, b_{1}=-2, c_{1}=4` and `a_{2}=18, b_{2}=17, c_{2}=4`

Using (a) we have,


`a_{1} a_{2}+b_{1} b_{2}+c_{1} c_{2}=(1)(18)+(-2)(17)+(4)(4)`


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