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## Homework Statement

hi

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 sin

^{2}Y to (1-cos

^{2}Y) 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!