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*What is the minimum distance between the point (3,-2,4) and the line defined by*

x = 1 + t

y = 4 - 3t

z = -2 + 2t

x = 1 + t

y = 4 - 3t

z = -2 + 2t

My approach was to find a point on the line by letting t = 1

I got (2, 1, 0)

then I found a vector between this point and the one given:

**v**= i -3j + 4k

Here's a picture to clarify:

Then the distance would be the scalar projection of this vector onto the normal vecor of the line

But I'm not sure how to find the normal to the line.

Could someone show me how?

And if there's a simpler approach could you show me that too?

Thanks.