# Solution - Equation of a Line in Space

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#### Question

If a line drawn from the point A( 1, 2, 1) is perpendicular to the line joining P(1, 4, 6) and Q(5, 4, 4) then find the co-ordinates of the foot of the perpendicular.

#### Solution

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A line passes through (2, −1, 3) and is perpendicular to the lines vecr=(hati+hatj-hatk)+lambda(2hati-2hatj+hatk) and vecr=(2hati-hatj-3hatk)+mu(hati+2hatj+2hatk) . Obtain its equation in vector and Cartesian from.

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Find the vector and Cartesian equations of the line through the point (1, 2, −4) and perpendicular to the two lines.

vecr=(8hati-19hatj+10hatk)+lambda(3hati-16hatj+7hatk) " and "vecr=(15hati+29hatj+5hatk)+mu(3hati+8hatj-5hatk)

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