3) Let two vector functions be defined by r₁(t) = (t², t, 3t³) r₂(t) = (t − 1,²—7,5 – t) - a. Find the intersection point of the functions. Is it a collision point? b. Find the equation of the line that goes through the intersection point that is also orthogonal to both curves at that point.

Q: 4. Write the vector equation for a line parallel to the line L: F = (1,-7)+t(2, -3), t € R…

A: Introduction: In three-dimensional geometry, a line can also be described through a vector equation,…

Q: X = Find the vector equation for the line of intersection of the planes x − 5y + 5z = −5 and x + 5z…

A: Given the equation of planes x-5y+5z=-5 and x+5z=1. To find the vector equation for the line of…

Q: Let L be the line through the point Q = (- 6, - 9, - 10) and direction vector d = [- 1, - 2, - 2]^T.…

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Q: Q2) Find the T „N of the vectors curve r(t) = at the point (1, 1)

A:

Q: (b) (c) Given that a(x)=0, show that ã•(¯ × (c − ã))=ã ● (ã×b). Hence, given that à =, b = and c =,…

A:

Q: The line (x-22-3, y = 2z) intersects the plane (x+3y-2+4= 0) at the point P, Find: a) the…

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Q: Find the vector equation of the line through the points P0(x0, y0, z0) and P1(x1, y1, z1).

A: P0x0, y0, z0 & P1x1, y1, z1. Now let a→ & b→ be the position vectors of the points P0x0, y0,…

Q: Find a vector equation for the line through the point P = (-3, 5, -4) and parallel to the vector v =…

A: