Question: 1. [10 Let E be the line in 3spaee that passes through the points A = (3, 1, 2) and B : (5, 4, 1).

1. [10 Let E be the line in 3spaee that passes through the points A = (3, 1, 2) and B : (5, 4, 1). (a) Find a set of parametric equations for B. (b)

Determine the set of all points on f whose distance from A

is at most half the distance from A to B. (e) Determine

1. [10 Let E be the line in 3spaee that passes through the points A = (3, 1, 2) and B : (5, 4, 1). (a) Find a set of parametric equations for B. (b) Determine the set of all points on f whose distance from A is at most half the distance from A to B. (e) Determine the value of k for which the point C = (k, k 1, k 6) lies on f. [(1) Determine the unique point D at which E intersects the plane with scalar equation 2131 + {122 2:3 : 3. Solve the following equation: (amaze)2 = 1000000053: Give your answer to 3 decimal places. 4 a) Solve y" ty'ty y = e-2* + sin3x + In5 - 4* + excos2x. [6] b) Solve the following second order ordinary differential equation y" - 4y' + 4y= 0 y(0) = -1 y'(0) = 1

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