i was wondering how exactly one should find the distance of a point to a line using cross product
for example, the distance from A(1,2,0) to a line running through B(0,1,2) & C(3,1,1) with Y being angle between BA and BC
BC = 3,0,-1
BA = 1,1,-2
so by using cross product formula, i get |BA|sin(Y) = |BAxBC| / |BC|
The Attempt at a Solution
i tried to calculate |BAxBC| by using the determinant method and i got 0, so the length = 0 too. how come?
so how do i compute the value |BAxBC| ? if i equate to |BA||BC|sinY, wouldn't it cancel out everything in the equation?
so i tried just calculating |BA|sinY by squaring & subsituting sin2Y to (1-cos2Y) and then using the dot product rule and then squarerooting it to get the answer sqrt3.5
so what have i done wrong? is my concept wrong? which way is correct? thanks!