How Can We Verify the Perpendicularity of Vector Products?

[wajed]

I have this question in my book:-

find the angle between the two vectors:
A= i - 2j + 3k
B= 2i + 3j -2k

the solution is based on the scalar product rule.. (so the question is solved)...

I`m just tryin to find another way to solve the problem? because I`m not really confident of vectors..

I have a questions also:-
Find the vector product of the two vectors:
A= i - 2j + 3k
B= 2i + 3j -2k
now the answer is: -5i+8j+7k..

now how could that resultant vector be perperndicular on A and B? it seems to have a "not right" angle (not 90 degree angle)..
because if the origion is 0,0,0.. then -5i +8j+7k makes a "non right" angle (it would only be right if the answer was 0,0,xk where x is any number)

if I`m mistaken about the origion being 0,0,0 then what is it?


by the way, I`ve asked this question on "Y! asnwers", but none answered, so I`m posting here..

 

[CompuChip]

I have this question in my book:-

find the angle between the two vectors:
A= i - 2j + 3k
B= 2i + 3j -2k

the solution is based on the scalar product rule.. (so the question is solved)...

I`m just tryin to find another way to solve the problem? because I`m not really confident of vectors..

If it makes you feel any better, you can draw them on a sheet of paper and use some geometry to find the angle... in the end you will end up using the exact same expression as you would using the inner product.

I have a questions also:-
Find the vector product of the two vectors:
A= i - 2j + 3k
B= 2i + 3j -2k
now the answer is: -5i+8j+7k..

now how could that resultant vector be perperndicular on A and B? it seems to have a "not right" angle (not 90 degree angle)..
because if the origion is 0,0,0.. then -5i +8j+7k makes a "non right" angle (it would only be right if the answer was 0,0,xk where x is any number)

First of all, (0, 0, xk) either does not make sense (when k is again a unit vector) or is confusing notation at the very best. I assume you meant x k = (0, 0, x).
Why do you think it should be along the z-axis? It would make a right angle with any vectors in the (x, y) plane. If you take for example A = i + j, B = 3i - 2j, you will see that the vector product A x B gives something pointing in the k-direction only. The vectors you gave have components along all three axes though. If you draw them on a piece of paper you will see that (A x B) is perpendicular to A (makes a right angle with A), as well as with B.

 

[wajed]

I got it, thank you,

"It would make a right angle with any vectors in the (x, y) plane. If you take for example A = i + j, B = 3i - 2j, you will see that the vector product A x B gives something pointing in the k-direction only."

Actually that was the problem, I was thinking of the first two vectors as being only on the x,y plane.

Thanx