Consider the line ly joining the points A(-5,-3,0) and B(7,1,4). 1. Find the parametric equation of...

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Consider the line ly joining the points A(-5,-3,0) and B(7,1,4). 1. Find the parametric equation of the line. 2. Show that the point C(1,-1,2) lies on the line. 3. Show that the point D(-4, 3, 2) is not on the line. 4. Find the foot of the perpendicular Q from D to the line and determine the shortest distance between the point and the line. 5. The line l intersects the line l given by r= 12i – 3j + 4k + (-8i + 3j – k). (a) Find the position vector of the point R of intersection. (b) Find the angle between the two lines. (c) Find the equations of the internal and external bisectors of the angle between the lines and l2. (d) The point D is on . Find a point D' such that DO = QD. (e) Find the equation of the line joining Rand D'. () Show that 4 is the bisector of angle DRD'. [Line 4 is the mirror image of the line a in l Consider the line ly joining the points A(-5,-3,0) and B(7,1,4). 1. Find the parametric equation of the line. 2. Show that the point C(1,-1,2) lies on the line. 3. Show that the point D(-4, 3, 2) is not on the line. 4. Find the foot of the perpendicular Q from D to the line and determine the shortest distance between the point and the line. 5. The line l intersects the line l given by r= 12i – 3j + 4k + (-8i + 3j – k). (a) Find the position vector of the point R of intersection. (b) Find the angle between the two lines. (c) Find the equations of the internal and external bisectors of the angle between the lines and l2. (d) The point D is on . Find a point D' such that DO = QD. (e) Find the equation of the line joining Rand D'. () Show that 4 is the bisector of angle DRD'. [Line 4 is the mirror image of the line a in l