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