# Problems from Distance between a straight line and a plane in space

Calculate the distance between the straight line and the plane:

$$r:(x,y,z)=(2,1,0)+k\cdot(1,4-3)$$

$$\pi:x+y+2z-1=0$$

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### Development:

Let's consider the governing vector of the straight line, $$\vec{v}=(1,4,-3)$$, and the normal vector of the plane, $$\vec{n}=(1,1,2)$$ and we do the scalar product: $$(1, 4, -3)\cdot(1, 1, 2) = -1 \neq 0$$\$ Therefore the straight line and the plane are not parallel and $$\text{d}(r,\pi)=0$$.

### Solution:

$$\text{d}(r,\pi) = 0$$

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