Find V x W?

Question

Find V x W if V = <2,1,-1> and W = <1,0,-2>

 

 

a. <2,-3,-1>

b. <2,0,2>
c. <2,1,2>
d. <-2,3,-1>

Answer 1

V x W = <2,1,-1> x <1,0,-2>

 

           = -2i + 3j -1k

 

           = <-2, 3, -1>

 

Answer d. <-2, 3, -1>

Answer 2

We can compute cross product by finding the determinant of this matrix:

i  j  k

2 1 -1

1 0 -2

Where i,j,k are the standard unit vectors.

 

Computing the determinant gives us: -2i + 3j - k

 

Which we can write as <-2,3,-1>

 

It is always a good idea to check your answers, the cross product should yield a vector perpendicular to both V and W.

<-2,3,-1>•V should be 0

<-2,3,-1>•W should be 0

 

Compute to determine that <-2,3,-1> is perpendicular to V,W and is indeed the cross product of V,W

Answer 3

So in order to find the cross product of 2 vectors, use the equations below:

 

V x W = <Cx,Cy,Cz>

 

Cx = VyWz − VzWy = 1×-2 − -1×0 = −2
Cy = VzWx − VxWz = -1×1 − 2×-2 = 3
Cz = VxWy − VyWx = 2×0 − 1×1 = −1

 

So, the answer is D.