Calculating Vector Lengths: The Dot Product and Pythagorean Theorem

[robertjford80]

Homework Statement

u =
[-.6]
[ .8]
compute the lengths ||u||

The Attempt at a Solution

I thought to compute ||u|| you multiply the absolute value of u * u then take the square root. That would be .6 * .8 which is .48 The square root of that is roughly .7 The book says the answer is 1 what am I doing wrong.

 

[SteveL27]

I thought to compute ||u|| you multiply the absolute value of u * u then take the square root.

Yes, assuming by '*' you mean the dot product.

That would be .6 * .8

No.

 

[robertjford80]

Why not? Saying no, doesn't help me. I already knew it was wrong. And yes I mean dot product.

 

[robertjford80]

never mind about this. i got the answer now.

 

[HallsofIvy]

The dot product of two vectors, <a, b> and <c, d>, is ac+ bd.

If $u= <u_x, u_y>$, u.u is NOT $u_xu_y$, it is $u_x^2+ u_y^2$
u.u= <-.6, -.8>.<-.6, -.8>= (-.6)^2+ (-.8)^3.

The length of vector <a, b> is $\sqrt{a^2+ b^2}$.