Find the distance the point P(-2,-4,-1) is to the line through the two points
Q(2,-1,0), and R(1,-3,-2).

I assume this is scalar projection, but is it PQ onto QR or PR onto QR or what?

Question

Find the distance the point P(-2,-4,-1) is to the line through the two points 
Q(2,-1,0), and R(1,-3,-2).

I assume this is scalar projection, but is it PQ onto QR or PR onto QR or what?

ganeshie8 · Answer

yes its just a projection, also you may work it without using projections :
$$\large   d = \dfrac{|\overrightarrow{QP} \times \overrightarrow{QR}|  }{|\overrightarrow{QR}|}$$

ganeshie8 · Answer

familiar with cross product, right ?

anonymous · Answer

yeah, this chapter is all on cross product

anonymous · Answer

or section, rather

ganeshie8 · Answer

then you may use above formula 
did u get why that formula gives the distance from point to line ?

anonymous · Answer

not exactly.  working out just what each vector is now before i use a formula.  Q-P etc

anonymous · Answer

the top part is the length of the cross product, but i don't get why you would divide by the other vector.

ganeshie8 · Answer

you're right!

ganeshie8 · Answer

cross product represents the area of parallelgoram

ganeshie8 · Answer

you might be knowing that already ?

anonymous · Answer

yes, that was the previous problem.  it was the distance of the cross product.

ganeshie8 · Answer

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