Question

Let L be the line with parametric equations

x = −6+2t
y = −8−t
z = −1+t
Find the vector equation for a line that passes through the point P(−9, −9, 2) and intersects L at a point that is distance 5 from the point Q(−6, −8, −1). Note that there are two possible correct answers. Use the square root symbol '√' where needed to give an exact value for your answer

Answer 1

To find the vector equation for a line that passes through the point P(-9, -9, 2) and intersects the line L, we need to find the point on L that is 5 units away from the point Q(-6, -8, -1). The vector equation of the line passing through P and intersecting L can be written as: r = P + t(Q - P), where r is the position vector of any point on the line, and t is a parameter.

Step-by-step explanation:

To find the vector equation for a line that passes through the point P(-9, -9, 2) and intersects the line L, we need to find the point on L that is 5 units away from the point Q(-6, -8, -1).

The vector equation of the line passing through P and intersecting L can be written as: r = P + t(Q - P), where r is the position vector of any point on the line, and t is a parameter.

Using the given values P(-9, -9, 2) and Q(-6, -8, -1), we can substitute the values into the equation to get the vector equation of the line passing through P and intersecting L.