Let L be the line with parametric equations

x = −10+2t
y = −2−t
z = 3t

Find the vector equation for a line that passes through the point P=P(5, 8, −9) and intersects L at a point that is distance 4 from the point Q=Q(−10, −2, 0). Note that there are two possible correct answers.

Question

Let L be the line with parametric equations

x = −10+2t
y = −2−t
z = 3t

Find the vector equation for a line that passes through the point P=P(5, 8, −9) and intersects L at a point that is distance 4 from the point Q=Q(−10, −2, 0). Note that there are two possible correct answers.

anonymous · Answer

Here are a few hints: Ray intersecting a sphere, parametric equation of a line can be converted to a vector equation of a line.