Find the parametric equation of the line that passes through P(1, 0, −3) and is parallel to the line with parametric equations x = −1 + 2t , y = 2−t, and z = 3+3t.

Which is the equation for y?

Parametric Equation = Type of equation that employs an independent variable called a parameter (often denoted by t) and in which dependent variables are defined as continuous functions of the parameter and are not dependent on another existing variable.

⇒ parametric equation of line passing through a point (a₁, b₁, c₁)

and parallel to a vector <a, b, c> is given by :

x =a₁ + at , y = b₁ + bt , z = c₁ + ct

now according to question:

given -

point, P(1, 0, -3)

line, x = −1 + 2t , y = 2−t, and z = 3+3t.

so from the line the vector is= <2, -1, 3>

now using above formula,

equation of line is = x = 1 + 2t , y = −t, and z = -3+3t.

we have to solve for 'y' only,

⇒ y = -t (answer)

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Find the parametric equation of the line that passes through P(1, 0, −3) and is parallel to the line with parametric equations x = −1 + 2t , y = 2−t, and z = 3+3t. Which is the equation for y?

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Find the parametric equation of the line that passes through P(1, 0, −3) and is parallel to the line with parametric equations x = −1 + 2t , y = 2−t, and z = 3+3t.

Which is the equation for y?