Question
Download Solution PDFWhat is the perpendicular distance from the point (2, 3, 4) to the line
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Dot product of two perpendicular lines is zero.
Distance between two points (x1, y1, z1) and (x2, y2, z2) is given by,
Calculation:
Let M be the foot of perpendicular drawn from the point P(2, 3, 4)
Let,
x = k, y = 0, z = 0
So M = (k, 0, 0)
Now direction ratios of PM = (2 - k, 3 - 0, 4 - 0) = (2- k, 3, 4) and direction ratios of given line are 1, 0, 0
PM is perpedicular to the given line so,
(2 - k) (1) + 3(0) + 4 (0) = 0
∴ k = 2
M = (2, 0, 0)
Perpendicular distance PM =
Hence, option (2) is correct.
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