3. (a) Two particles travel along the curves ř1 (t) = (t² + 3, t+1,6/t), ř2(u) = (4u, 2u – 2, u² – 7). Find the points were the particles collide and the points where the paths intersect. At a point of intersection that is not a collision point find the angle between the tangent lines. (b) Find parametric equations for the line tangent to the helix r(t) = (/2 cos t)ĩ+ (/2sin t)j + tk at the point where t = }. At which points on the helix are the tangent lines perpendicular to the line x = y, z = 0?

Q: Find parametric equations for the line through the point P(3, 6, 4) that is parallel to the plane x…

A:

Q: A) Find the parametric equations for the line through the point P = (3.-5, 1) that is perpendicular…

A:

Q: Find a set of parametric equations for the curve of intersection of the cylinder (x - 1)2 + y2/4 = 1…

A: Given: The equation of cylinder is: x-12+y24=1 .....(1) The equation of paraboloid is: x2+y-22=z…

Q: Find the distance between point A(-1,4,6) and the line of parametril equations x = 2-3t, y = -4+t, z…

A:

Q: Find the equation of the plane passing through the point P(2, -1, 3) and perpendicular to the line…

A: We have to find the equation of the plane passing through the point  and perpendicular to the line…

Q: Suppose parametric equations for the line segment between (7, 4) and (0, 6) have the form: S#(t)…

A: Values of constants

Q: Suppose parametric equations for the line segment between (8, 10) and (4, 1) have the form: a + bt…

A: Given that the points 8,10 and  4,1

Q: 3. What is the parametric equation for the line through the point (1 ,2, 3) parallel to the x- axis?…

A:

Q: ) (i) Find the parametric equations for a smooth curve, C: x= 4z, y = -3z that joins two points,…

A:

Q: Are the statements P → (Q ∨ R) and (P → Q) ∨ (P → R) logically equivalent? Prove your answers using…

A: