Write the value of `k` for which the line `(x-1)/2=(y-1)/3=(z-1)/(k)` is perpendicular to the normal to the plane ` vec rdot((2 hat i+3 hat j+4 hat k)=4.`

Explanation

Given: The value of `k`
for which the line `(x-1)/2=(y-1)/3=(z-1)/(k)`
is perpendicular to the normal to the plane ` vec rdot((2 hat i+3 hat j+4 hat k)=4`

Now, ` vec ndot((2 hat i+3 hat j+4 hat k)=4`

`a1=2,b1=3,c1=4`

`a1cdot a2+b1cdot b2+c1cdot c2=0`

`implies 2cdot2+3cdot3=4cdotk=0`

`implies 4+9+4k=0`

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