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- Find the vector equation of a line L going through the point P = (-5, -6) and parallel to the line generated by multiples of the vector v = --HA 1 L(t) - +tFind the scalar equation of the line = (-3,4) +t(4,-1).Find the cartesian equation of the straight line tangent to the plane curve given by the vector equation r(t) = (t- 6) i + + 3t - 2) į. at the point P(-5,4) on the curve. Express your answer in the form y = ax + b , where a and b are integers. equarion of the tangent line is given by y = 9x + 49
- Express the vector = + y. F 10 as a linear combination of -[-] and ÿ==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 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.
- The path r(t) = (t) i + (3t2 +7) į describes motion on the parabola y = 3x + 7. Find the particle's velocity and acceleration vectors at t= - 4, and sketch them as vectors on the curve. The velocity vector at t= - 4 is v(- 4) = (D i+ (Di (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)For this problem, enter your vectors with angle-bracket notation: , not in ijk- notation. (a) F = 7xi + (8y – z2) j + (2x + 15z) k - F does not have a vector potential H, H = none (If there is no potential function, enter none for the function.) (b) F = 7xi + (8y – z?) j + (2x – 15z) k F has a vector potential + Ĥ, Ĥ = (If there is no potential function, enter none for the function.)Create the vector & parametric equations for the line that passes through the point L₁ x 3- 2t (0, 1, -2) and is parallel to the line y z = = - 5t - 1-t.