(a) For the line l in R2 given by the equation ax + by = d, find a vector v that is para...

(a) For the line l in R² given by the equation ax + by = d, find a vector v that is parallel to l. (b) Find a vector n that is normal to l and has first component equal to a. (c) If P₀(x₀, y₀) is any point in R², use vectors to derive the following formula for the distance from P₀ to l:

To do this, you’ll find it helpful to use Figure 1.115, where P₁(x₁, y₁) is any point on l. (d) Find the distance between the point (3, 5) and the line 8x − 5y = 2.