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Find the distance of the point 2i - j - 4k from the plane vector r.(3i - 4j +12k) - 9 = 0.

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Best answer

Given:

Point given by the equation: \(\vec a=2\hat i-\hat j-4\hat k\)

Plane given by the equation:  \(\vec r.(3\hat i - 4\hat j+12\hat k)-9=0,\) 

 where the normal vector is: \(\vec n=3\hat i-4\hat j+12\hat k\)

We know, the distance of  \(\vec a\) from the plane \(\vec r.\vec n-d=0\) is given by:

the distance of the point  \(2\hat i-\hat j-4\hat k\) from the plane.

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