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10 cards from this deck
r=a+λb\mathbf{r} = \mathbf{a} + \lambda \mathbf{b}r=a+λb
A point on the line
Direction vector of the line
Normal vector to the plane
Substitute line eqn into plane eqn
Substitute λ\lambdaλ back into line eqn
ax+by+cz+d=0ax + by + cz + d = 0ax+by+cz+d=0
∣ax1+by1+cz1+d∣a2+b2+c2\frac{|ax_1 + by_1 + cz_1 + d|}{\sqrt{a^2 + b^2 + c^2}}a2+b2+c2∣ax1+by1+cz1+d∣
∣ax1+by1+cz1+d∣|ax_1 + by_1 + cz_1 + d|∣ax1+by1+cz1+d∣
a2+b2+c2\sqrt{a^2 + b^2 + c^2}a2+b2+c2
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