How are these vector equations equivalent?

[Calpalned]

Homework Statement

My solutions manual states that (1 - t)(2i - j + 4k) + t(4i + 6j + k) = (2i - j + 4k) + t(2i + 7j -3k), 0 < t < 1.

Homework Equations

r(t) = (1 - t)r₀ + tr₁

The Attempt at a Solution

I don't see how they are equivalent. They can't be divided because one has i, j and k and the other has t.

 

[Brian T]

Try simplifying the left side and see what you get

 

[Chestermiller]

What they wrote is just the summation of the two vectors, component-by-component. Which part don't you understand?

Chet