Interpreting Linear Algebra Equation

[NSOutWest]

I've been given a parametric equation (forgive me if this is the wrong term) of the form

[x₁, x₂, x₃] = [1, 2, 3] + t[1, 1, 1]

and I don't know how to interpret it.

My best guess:

1x₁ + 2x₂ + 3x₃ + t(x₁ + x₂ + x₃)

I know this isn't right; could someone help me out?

EDIT: "t" is simply an arbitrary variable.

 

[Ray Vickson]

I've been given a parametric equation (forgive me if this is the wrong term) of the form

[x₁, x₂, x₃] = [1, 2, 3] + t[1, 1, 1]

and I don't know how to interpret it.

My best guess:

1x₁ + 2x₂ + 3x₃ + t(x₁ + x₂ + x₃)

I know this isn't right; could someone help me out?

EDIT: "t" is simply an arbitrary variable.

It means that the vector on the left of the "=" sign equals the vector on the right, and that means that the first component on the left must equal the first component on the right, etc. In other words, for any i, the i-th component on the left equals the i-th component on the right.

RGV

 

[NSOutWest]

Okay, I figured it out (with a buddy's help).

The first part is a point (Duh, don't know how I missed that one.), and the second part is a vector of length t(x, y, z). Adding them together gives a vector with an origin.