Dot Products of Vectors - Please help me understand....

Hi there.

I am working through a worksheet, however my knowledge of mathematical symbols is not very sound.

Here is the problem. (P1 and P2 are Point 1 and Point 2 respectively.)

T1 is a Tangent.

P1 := 0 , 0 , 0 (xyz)

P2 := 73.14 , 55.84 , 38.44

T1 := 0.6409 , 0.6409 , 0.42

I have to find a number from the following equation:

Ψ² = dist between points

η = perp dist from P1 in dir of T1

ξ = dist normal to T1

Ψ² = |P2 - P1|²

η = (P2 - P1) · T1

ξ = (Ψ² - η²)^0.5

Please tell me if my findings are true.... I have no idea how to calculate these vectors!

I understand they are dot products, but there don't seem to be any 'layman' explainations on the web.... Here's what I solved:

Ψ² = 3592.88

η = 7.73

ξ = 59.44

Can anyone tell me if I'm correct? I'm 99% sure it's incorrect, as a following equation produces an error based on the square root of a negative number.

I would be so grateful if someone could walk me through it!

Thanks!