Vector Components and Dot Product Proof

[bossman007]

Homework Statement

A is a vector

Show that: a1 = x hat (dot) A
a2 = y hat (dot) A
a3 = z hat (dot)A

Homework Equations

A= (a1*x hat) + a2*y hat) + (a3* z hat)

The Attempt at a Solution

my hint says to take the dot product of both sides of the equation in (2) with each of the basis vectors in turn.

Doing this I get A^2 = [(a1*x hat) + a2*y hat) + (a3* z hat)] dot A

I don't know what to do next, or if that's even right.

 

[Mark44]

Homework Statement

A is a vector

Show that: a1 = x hat (dot) A
a2 = y hat (dot) A
a3 = z hat (dot)A

You haven't told us what a₁, a₂, and a₃ are, nor have you said what "x hat" and the other two hats represent.

Don't make us try to read your mind...

Homework Equations

A= (a1*x hat) + a2*y hat) + (a3* z hat)

Is this given? If so, you need to say so.

The Attempt at a Solution

my hint says to take the dot product of both sides of the equation in (2) with each of the basis vectors in turn.

Doing this I get A^2 = [(a1*x hat) + a2*y hat) + (a3* z hat)] dot A

I don't know what to do next, or if that's even right.

A² has no meaning - you can't just multiply a vector by itself. You can dot it with itself, but you don't get A².

 

[LCKurtz]

Are $\hat x, \hat y, \hat z$ the unit vectors in the x,y, and z directions, more commonly known as i, j, and k? And is $\vec A = a\mathbf{i} +b\mathbf{j} + c\mathbf{k}$? If so, the problem is pretty easy. Remember the basis vectors are perpendicular. What happens if you dot i into both sides?

 

[bossman007]

I tried what I thought you meant to try, here's what I did. I dotted both sides of the equation by x-hat in my case instead of ur i-hat example. Here's what I got. Dunno if on right track or not.

[PLAIN]http://postimage.org/image/6zbkosjsp/ [/PLAIN]

 

[Muphrid]

What do you think $\hat x \cdot \hat x$ is?

 

[bossman007]

x hat dot x hat = x^2

 

[Muphrid]

Mm, nope. What is the significance of the hat? What does a hat tell us about a vector?

 

[bossman007]

that it's a unit vector , which equals one?

so x-hat (dot) x-hat = 1?

 

[Muphrid]

That it's a unit vector, so its length is 1. Dot product of a vector with itself gives the length squared, but $1^2 = 1$, so yeah.