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- Find the vector equation of the line that passes through the point (1, 5) and is parallel to the line r = (3 + 7t)i + (1 − 3t)j.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 vector form of the equation of the line in R2 that passes through P= (2, - 1) and is parallel to the line with general equation 2x -3y = 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 + 49Find the vector form of the equation of the line in R2 that passes through P = (2, -1) and is perpendicular to the line with general equation 2x - 3y = 1.Find the vector equation of the line that contains the points (-5, 17,9) and (-17,10,2). r(t) = ( ) +t ( 9 "
- Find a vector equation for the line through the point P = (-3, 5, -4) and parallel to the vector v = (5, -1, 1). Assume r(0) = -3+5-4k and that v is the velocity vector of the line. k r(t) =Find the scalar equation of the line = (-3,4) +t(4,-1).Determine a vector equation for the line that is perpendicular to 7 = (4, 1) + s(−3, 2), sER, and passes through point P(6, 5).
- At time t = 0, a particle is located at the point (4,8,6). It travels in a straight line to the point (1,7,2), has speed 2 at (4,8,6) and constant acceleration - 3i -j- 4k. Find an equation for the position vector r(t) of the particle at time t.The equation r(t) = (3t + 5) i+ (4t - 5) j+ (4t) k is the position of a particle in space at time t. Find the particle's velocity and acceleration vectors. Then write the particle's velocity at t=0 as a product of its speed and direction. What is the velocity vector? v(t) = ( 3) i+ ( 8t) j+ (4) k What is the acceleration vector? a(t) = (0) i+ (8) j+ (0) k Write the velocity vector at t= 0 as a product of the speed and direction. 8 v(0) = (/89 i+ V89 j+ V89 V89 (Type exact answers, using radicals as needed.)Find a vector equation for the line segment from (Use the parameter t.)(2, −1, 4) to (5, 5, 1)