Determine the value of `lambda` for which the following plane are perpendicular to each other. `2x-4y+3z=5\ a n d\ x+2y+lambdaz=5`

Explanation

Here, In planes,

`2 x-4 y+3 z=5 `and `x+2 y+lambda z=5`

`a_{1}=2, b_{1}=-4, c_{1}=3` and `a_{2}=1, b_{2}=2, c_{2}=lambda`

are perpendicular to each other if


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

`Rightarrow 2 times 1+(-4) times 2+3 times lambda=0 `

`Rightarrow 2-8+3 lambda=0 `

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