A line passing through the point A with position vector ⇁a=4^i+2^j+2^k is parallel to the vector ⇁b=2^i+3^j+6^k. Find the length of the perpendicular drawn on this line from a point P with vector ⇁r1=^i+2^j+3^k.
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Solution
Given position vector
→a=4^i+2^j+2^k
parallel vector
→b=2^i+3^j+6^k
eq of line
→r=4^i+2^j+2^k+λ(2^i+3^j+6^k)
Point P(1,2,3)
let a line from point P(1,2,3) meets the vector at point Q(x,y,z) on given line perpendicularly