(VECTORS) Find (alpha), (beta), and (gamma)

[lvvin]

If a = 3i - 2j + k, b = -2i + 5j + 4k, c = -4i + j + -2k and d = 2i - j + 4k,

determine (alpha), (beta), and (gamma) such that d = (alpha)a + (beta)b + (gamma)c

I'm not sure how to get started on this question. It would be greatly appreciated if working could be displayed for better understanding. Thank you.

 

[Dr.Peterson]

The most natural method for you depends on what you are learning; you haven't told us anything by which to determine that.

One elementary way is to plug the definitions of a, b, c, and d into [MATH]d=\alpha a+\beta b+\gamma c[/MATH], and write a system of equations (one each for i, j, and k), then solve it for variables [MATH]\alpha[/MATH], [MATH]\beta[/MATH]. and [MATH]\gamma[/MATH].

 

[Deleted member 4993]

If a = 3i - 2j + k, b = -2i + 5j + 4k, c = -4i + j + -2k and d = 2i - j + 4k,

determine (alpha), (beta), and (gamma) such that d = (alpha)a + (beta)b + (gamma)c

I'm not sure how to get started on this question. It would be greatly appreciated if working could be displayed for better understanding. Thank you.

So:

αa = 3α i - 2α j + α k

ßb = ?

Γc = ?

Now add those up and continue......