At what point do the curves r₁(t) = (t, 2 − t, 15 + t²) and r₂(s) = (5 – s, s − 3, s²) intersect? (x, y, z) = Find their angle of intersection, 0, correct to the nearest degree. 0 = O

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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r1(t) = t, 2 − t, 15 + t2 and r2(s) = 5 − s, s − 3, s2
At what point do the curves intersect?
(x, y, z) = 
Find their angle of intersection, ?, correct to the nearest degree.
? =
At what point do the curves r₁(t) = (t, 2 − t, 15 + t²) and r₂(s) = (5 – s, s − 3, s²) intersect?
(x, y, z) =
Find their angle of intersection, 0, correct to the nearest degree.
0 =
O
Transcribed Image Text:At what point do the curves r₁(t) = (t, 2 − t, 15 + t²) and r₂(s) = (5 – s, s − 3, s²) intersect? (x, y, z) = Find their angle of intersection, 0, correct to the nearest degree. 0 = O
Expert Solution
Step 1

Given curves:

r1t = t, 2-t, 15+t2

r2s=5-s, s-3, s2

To find:

a) The point of intersection of both the curves.

b) Angle between them.

Angle between the direction vectors u and v:

θ=cos-1u·vuv

Here, u·v denotes the dot product of the two vectors.

It is defined as u·v=a1a2+b1b2+c1c2, where u=a1,b1,c1 and v=a2,b2,c2.

u = a12+b12+c12 and v = a22+b22+c22.

 

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