Find parametric equations for the line through point P(2,-4,2) in the direction of the vector (5,-6,-5).

The parametric equations are:

x(t) = 2 + 5t

y(t) = -4 - 6t

z(t) = 2 - 5t

Step-by-step explanation:

The equation can be written as:

P = Po + vt

Where Po is the point (2, -4, 2)

V is the direction vector (5, -6, -5)

The equation above becomes

P = (2, -4, 2) + (5, -6, -5)t

P = (2, -4, 2) + (5t, -6t, -5t)

P = (2+5t, -4-6t, 2-5t)

The parametric equations are therefore:

x(t) = 2 + 5t

y(t) = -4 - 6t

z(t) = 2 - 5t

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step-by-step explanation: