The Missing Vector

Algebra Level 3

How many solutions for vector $[a,b,c]$ are there such thnat

$[2,3,4] \times [a,b,c] =[1,2,-2] ?$

Note that this is a cross product.

Only 1 Infinite up to 10 None

1 solution

Viraj Tamakuwala
Jan 6, 2016

First Find is there a solution to this or not...

We can do this by doting [2,3,4] and [1,2,-2]

= 2 · 1 + 3 · 2 + 4 · (-2)

= 2 + 6 - 8

= 0

Therefore there is a solution.

Now Cross Product [2,3,4] X [a,b,c]

You get the following equations

3c-4b = 1

4a-2c = 2

2b-3a = -2

//You can isolate in terms of another variable

Isolate "c" in terms of a

c = 2a -1

Isolate "b" in terms of a

b = 1.5a - 1

Plug them in eq " 3c-4b = 1"

3(2a-1)-4(1.5a-1) = 1

6a - 3 - 6a + 4 = 1

6a -6a = 1+4-3

0a = 0 //Should end like this

This means "a" can be any value and therefore have infinite solutions