| Posted on Saturday, 06 December, 2003 - 03:44 pm: |
1) find the components of the two unit vectors
w=(w1,w2,w3) which make an angle of 60 degrees with the vector u=(1,0,-1) and an angle of 45 degrees with the vector v=(1,-2,-2).
2) show that these two unit vectors are perpendicular.
| Posted on Saturday, 06 December, 2003 - 05:13 pm: |
Do you know the dot product? I'll denote vectors in bold. It says that v.w = |v||w|a, where a is the angle between these vectors. Also, if a=(x,y,z) and b=(x¢,y¢,z¢) then a.b=x x¢+y y¢+z z¢. Try to use this.
| Posted on Saturday, 06 December, 2003 - 05:26 pm: |
I think you mean v.w=|v||w|cosa where a is the angle between them.
| Posted on Saturday, 06 December, 2003 - 07:23 pm: |
Of course I did.
| Posted on Sunday, 07 December, 2003 - 01:23 am: |
I still can't solve it. There are too many variables. I don't understand.
| Posted on Sunday, 07 December, 2003 - 10:12 am: |
Ok. We know that
= 1.We have
.Similarly,
.Finally, we have
.Now you only have to solve this system.
| Posted on Sunday, 07 December, 2003 - 10:35 am: |
So, we have to solve the system
.Subtract the first two equations to get
.So we get
.Hence
.So we then get
Hence
or 
.The corresponding vectors are
and
.It is easy to check that they are orthogonal:
