Dot product?

[Rijad Hadzic]

Homework Statement

Im given vectors:

b = x hat + y hat
c = x hat + z hat

Homework Equations

http://imgur.com/a/iHTOT

The Attempt at a Solution

so I have 2 eq's... one says:
r * s = rscos(theta)

the other is a summation saying multiply x component 1 with x component 2, add y component 1 with y component 2, and so on.

Ok so I start with method 2: 1*1 x hat + 1* 0 y hat + 0*1 z hat

so you end with 1 (my books answer).

But when I use "r * s = rscos(theta)" I find the angle between them is 90 degrees so I get 0.

Whv does 1 formula work in this case but the other doesnt

 

[Mark44]

Homework Statement

Im given vectors:

b = x hat + y hat
c = x hat + z hat

Homework Equations

http://imgur.com/a/iHTOT

The Attempt at a Solution

so I have 2 eq's... one says:
r * s = rscos(theta)

the other is a summation saying multiply x component 1 with x component 2, add y component 1 with y component 2, and so on.

Ok so I start with method 2: 1*1 x hat + 1* 0 y hat + 0*1 z hat

No, this isn't what it is saying. What you get from a dot product is a number -- no vectors involved.

There are two forms for the dot product of vectors in $\mathbb{R}^3$: one that involves the cosine of the angle between the vectors, and the other that involves the sum of the products of the components.

Assuming these are your vectors. $\vec r = <1, 1, 0>$ and $\vec s = <1, 0, 1>$, then $\vec r \cdot \vec s = 1 \cdot 1 + 1 \cdot 0 + 0 \cdot 1 = 1$

so you end with 1 (my books answer).

But when I use "r * s = rscos(theta)" I find the angle between them is 90 degrees so I get 0.

Whv does 1 formula work in this case but the other doesnt

Both formulas work, but the angle between the two vectors is not 90° - they are actually 60° apart.