Find Vector C when given Vector A & B.

[ichivictus]

This is from Schaum's 3000 solved Physics problems (1.75). The teacher attempted to guide us to solve it but me and a few classmates are still struggling to figure this out.

Homework Statement

Vector A = 3i + 5j - 2k
Vector B = -3j + 6k
Find a Vector C such that 2A + 7B + 4C = 0

The Attempt at a Solution

This looks a lot like Linear Algebra, something I am not particularly skilled in, however I think I gave it a decent shot.

Ax = 3
Ay = 5
Az = -2

Bx = -3
Bz = 6

2(3) + 7(-3) + 4(Cx) = 0
Cx = 15/4 = 3.75

2(5) + 0 + 4(Cy) = 0
Cy = -10/4 = -5/2 = -2.5

2(-2) + 7(6) + 4(Cz) = 0
Cz = -38/4 = -19/2 = -9.5

So therefor Vector C = (15/4)i - (5/2)j - (19/2)k

The real solution is C = -1.5i + 2.75j - 9.5k

Looks like I got Cz correct, but I can't figure out how to get Cx and Cy.

 

[jedishrfu]

First off your B components are wrong Bx=0 By=-3 and Bz=6

and you have three equations to get the three C components:

2Ax + 7Bx + 4Cx = 0

2Ay + 7By + 4Cy = 0

2Az + 7Bz + 4Cz = 0

so its simple algebra from here

 

[CWatters]

Ax = 3
Ay = 5
Az = -2

Bx = -3
Bz = 6

Should be By=-3 not Bx ?

Edit: jedishrfu beat me to it.

 

[ichivictus]

Oh simple mistake ha. Thanks!