# At what point do the curves r1(t) = t. 4 − t. 63 + t2 and r2(s) = 9 − s. s − 5. s2 intersect?

At exactly what point perform some curves r1(t) = t, 5 − t, 63 + t2 and r2(s)
= 9 − s, s − 4, s2 intersect? At exactly what point perform some curves r1(t) (t, 5-t, 63 t2) and r20s) (9 s, S 4, s2) in (x, y, z) Get a hold of their particular perspective of intersection, 0, proper to your closest level.

Both curves r1 and r2 come in the 3
dimentional (x,y,z) jet
All Curves cannot satisfy. To confirm whether or not they satisfy at an original
point, we have to equate the x, y and z aspects of a spot
Equating the x aspects of things for the curves
t=9-s s+t
=9………….(1)
Equating the y aspects of the things both for curves
5-t = s-4 s+t
=9 …………..(2) (the exact same appearance formerly gotten)
Equating the z elements
63+ t2 =
s2………………………….(3)
From equation (2) we are able to
compose s = 9-t
placing the worthiness of s in
equation (3), we have 63+ t2 =81 -18t +
t2
Cancelling the
t2 on both edges associated with preceding equation, we have 63 =
81-18t
Thus the worthiness of t is available is 1
From equation (1), the worthiness of s = 8 whenever t = 1
Through the use of these values of t and s, we have the point of
intersection is (1,4,64)
To obtain the perspective involving the curves, we must discover dot
services and products of pitch associated with tangent. Thus we are able to get a hold of cosine of perspective
among them.
The differenciation of r1 wrt t and r2 wrt
s provides <1,-1,2t> and <-1,1,2s> as element of
mountains associated with tangent

<1,-1,2> and <-1,1,16> correspondingly
Dot item of 2 amounts u and v is u.v =|u||v cos =
1*(-1) + -1*1+ 2*16 = 30
Thus cos = u.v/|u||v| =

0.7624
Cos-1 (0.7624) = 40.3
Thus the perspective of intersection proper to closest level is
40        