A. Find the vector equation of a line tangent to r(t) = (t², t², t³) at t = 1. B. Determine whether or not a line tangent to r(t) = (t², t², t³) at t = 1 will in line through (2,2,3) in the direction = (3,-2,-1). Find the point of inters exists. C. Determine whether particles travelling along a line tangent to r(t) = (t², t², 1 and the line through (2,2,2) in the direction v = (3, —2, −1) would collide not collide if these lines intersect

Q: (9.) r(t) = (1, cos t, 2 sin t)

A: As per your query the solution of question no 9 is given the next step.

Q: Q.7: find the directional parametrization of the line segment joining two point A(2,1,3) and…

A: It is a basic questions of 3-D geometry , we have equate the equation only

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A: The direction derivative  of f(x,y) in the direction of unit vector, is defined as follows.

Q: Find a vector function that represents the curve of intersection of the paraboloid z = 5x² + 2y² and…

A: The paraboloid z=5x2+2y2 and the cylinder y=3x2. We have to find a vector function that represents…

Q: Given the points A(2,6,0) and B(3,5,6) determine the equation of a line vector in parametrix form

A:

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

A:

Q: 2) Let two vector functions be defined by r₁(t) = (2t, t², t²) r₂(t) = (sint, sin(3t),5t) a. Find…

A: a. Consider the given vector functions, r1(t)=2t,t2,t4r2(t)=sint,sin3t,5t if two vector function…

Q: C:r=r(t)=(1+t,2 – 3t, 4t)

A: We Have :— X = 1 + t Y = 2 — 3t Z = 4t

Q: Find a vector equation for the line through the point (2, 5, 8) perpendicular to the plane 2x + 5y +…

A:

Q: Which of the following is the equation of the plane passing through the point (0,2,-3) and with…

A:

Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t= 0. Q…

A: