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 The distance dd of a point P to the line through points A and B is the length of the component of AP that is orthogonal to AB, as indicated in the diagram. So the distance from P=(3,−4,5) to the line through the points A=(4,2,−2) and B=(−2,0,5) is
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Step 1

Given,

The distance d of a point P to the line through points A and B is the length of the component of AP that is orthogonal to AB, as indicated in the diagram.

Step 2

Here, we have P = (3, −4, 5), A = (4, 2, −2) and B = (−2, 0, 5).

Now, help_outlineImage TranscriptioncloseThe component PA is b = (4 - 3,2 (-4),-2 - 5) = (1,6,-7) And AB a (-2 - 4,0 2,5- (-2) ) - (-6,-2, 7) fullscreen
Step 3

Therefore, the distanc... help_outlineImage Transcriptionclosed laxb lal j k 6 2 7 6 -7 |(-6)2+(-2)2+72 li(14-42)-(42-7)+k(-36+2)| V36+4+49 |-28i-j35-34k| /36+4+49 /784+1225+1156 68 3165 V89 3156 89 fullscreen

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