Consider line L, given below. x = 9 + t, y = 7 + t, z = 5 + 4t, t is in ℝ (a) Find point P that belongs to the line and direction vector v of the line. Express v in component form. P = Correct: Your answer is correct. v = Correct: Your answer is correct. (b) Find the distance from the origin to line L.

Step-by-step explanation:

(a)

The equation of the line, L is given by x = 9 + t, y = 7 + t, z = 5 + 4t; where t is a real number.

In the above equation, if we put t = 0, then x = 9, y = 7 and z = 5.

Hence, the point (9, 7, 5) lies on the given line. We can say it as P.

The direction vector, v is {1, 1, 4}.

(b)

The equation of the given line can also be written as .

The vector, OP = (9, 7, 5), where O is the origin.

The direction vector v = {1, 1, 4}.

The cross product of OP and v is = {23, -31, 2}.

Hence, the distance is ≅9.