# IB Vectors: Find scalars

• Feb 9th 2008, 01:50 PM
overduex
IB Vectors: Find scalars
Two vectors are defined as a= (-3, 1, 4) and b= (6, -6, -5). Find values of the scalars X and Y if Xa+Yb is equal to:
(-36, 32, 33).

I would really like to attempt this problem myself. So, If anyone could please explain how to solve I would really appreciate it!
• Feb 9th 2008, 07:19 PM
mr fantastic
Quote:

Originally Posted by overduex
Two vectors are defined as a= (-3, 1, 4) and b= (6, -6, -5). Find values of the scalars X and Y if Xa+Yb is equal to:
(-36, 32, 33).

I would really like to attempt this problem myself. So, If anyone could please explain how to solve I would really appreciate it!

I've left enough gaps for you to lay some claim to the solution for yourself:

On the one hand, X(-3, 1, 4) + Y(6, - 6, -5) = (-3X + 6Y, ...........)

But on the other hand X(-3, 1, 4) + Y(6, - 6, -5) = (-36, 32, 33).

Therefore:

-3X + 6y = -36 .... (1)

..... (2)

....... (3)

Equations (1), (2) and (3) are to be solved simultaneously for X and Y. Choose two of the equations and solve. Check that the resulting solutions satisfy the third equation (if they didn't, then there'd be no solution at all - all three equations have to be satisfied).