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- Give a vector parametric equation for the line through the point (-5, -2, 1) that is parallel to the line (3t - 4, 4t - 2, 2t - 4): L(t) =Find both the parametric and vector equation of the line segment between (−2, 3) and (5, −1) where 0 ≤ t ≤ 1. Please show all your work.Find both the parametric and vector equation of the line segment between (−2, 3) and (5, −1) where 0 ≤ t ≤ 5. Please explain your steps. Thank you.
- Find the parametric equations of the tangent line to the curve represented by the vector function 7 (t) = (-3+ 2t – 2t², 2 – t, 3t) at the point (–7,0, 6).Find the parametric equations of the tangent line to the curve represented by the vector function r(t) = (9t+9, -3t² - 5t-5, -t³-2t² - 1) at the point (27, -27, -17).Provide the parametric equations of the normal line to the surface defined by the vector equation given at the point (0,0,π).
- The vector parametric equation for the line through the points (2, -5, 5) and (3, −5, −4) is L(t) =5. (a) (b) The surfaces (x − 2)² + z² = 9 and y - Find a vector equation for the curve C. = z² intersect along the curve C. Find parametric equations for the tangent line to this curve at (2, 9, 3).4. a) Find an equation of the line that is tangent to the curve given by the vector-valued function 7(t) the parametric equations of the line.) b) Find the distance of the point (1,0, – 1) from the plane 2x+y+z+3= 0. t3 t2 3' 2 ? ,t > at the point (,, 1). (You can give =< 3' 2'
- The path r(t)=(5 sin t) i+(5 cos t) j describes motion on the circle x^2+y^2=25. Find the particle's velocity and acceleration vectors at t=π/3 and π/6, and sketch them as vectors on the curve.generate a parametrization of the line through P(2, -4, 7) parallel to v1 = 2i - j + 3k. Then generate another parametrization of the line using the point P2(-2, -2, 1) and the vector v2 =-i + (1/2)j - (3/2)k.Parameterize the line from (1,5) to (-4, -3) so that the line isat (1, 5) at t=0 and at (-4,-3) at t=1. y= Your parametric equation should be linear functions of t.