Finding angle through cross and dot product

[cxiangzhi]

By using both cross and dot products, the angle between 2 vectors can be found. But there is 1 question that I tried for countless times that the result of cross product and dot product are not the same.

Here is the vectors that I am talking about

A= 2i+3j=k
B= -4i+2j-k

The result by using dot product = 100.08°
The result by using cross product = 79.92°

 

[voko]

What is 2i+3j=k?

Show your steps.

 

[cxiangzhi]

My mistake. Its A= 2i+3j+k

AxB=-5i-2j+16k

abs(AxB) = 16.88

abs(AxB)=abs(A) x abs(B)sinθ

∴ abs(AxB)/(abs(A) x abs(B))= sinθ
∴ θ = 79.92

A.B=-3

A.B/(abs(A) x abs(B))= cos(theta)

∴θ = 100.08

The result of dot and cross product should be the same but its not in this case. Please help.

 

[great_sushi]

Are you using matrices to solve the cross product?

 

[cxiangzhi]

Yeap.. I used the determinant method to solve the cross product..

 

[voko]

Observe that sin 79.92 = sin 100.08. So the cross product per se cannot distinguish between such angles.

 

[cxiangzhi]

Im sorry but I still have a question here.. What is per se?

 

[NemoReally]

Im sorry but I still have a question here.. What is per se?

A Latin language phrase meaning "in itself" (or "by its nature").

http://en.wikipedia.org/wiki/List_of_Latin_phrases_(P)#per_se

 

[cxiangzhi]

Thanks a lot guys.. Appreciate you help.. :)