If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from a point P to the line L is equal to the length of the component of the vector AP that is orthogonal to the vector AB. A Use the method above to find the distance from the point P(-3, 1,7) to the line through A(1, 1.0) and B(-2,3.-4).

Consider (13,3,7) in vector space. Find symmetric equations of a line that contains the point (13,3,7) and the origin. Demonstrate how to check (13,3,7) and (0,0,0) that they fit the equation of the line.

P(2,5, 4) and Q(8,3,3) Let be the line through P in vector direction (1,2,3) and let II be the plane through Q perpendicular to (4,-1,-9). Find an equation for II.

16. Determine the vector equation of each line. a) parallel to the y-axis and through Po(-4, 11) b) perpendicular to 5x - 2y = 3 and through Po(7, 1) c) parallel to x + 6y = 1 and through Po(2,-5) d) parallel to the z-axis and through Po(-4, 3, 7) e) parallel to [x, y, z]= [1, 3, -2] + [5, 2, 1] f) the x-intercept of the line is 3 and the y-intercept is -2