Calculating Vector Lengths: The Dot Product and Pythagorean Theorem

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Homework Help Overview

The discussion revolves around calculating the length of a vector using the dot product and the Pythagorean theorem. The original poster presents a vector and attempts to compute its length, leading to confusion regarding the correct method.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to compute the vector length using a method involving multiplication of components and taking the square root, leading to an incorrect result. Some participants clarify the definition of the dot product and the correct formula for vector length, while others express frustration over the lack of constructive feedback.

Discussion Status

The discussion has seen attempts to clarify the computation of the dot product and the formula for vector length. While one participant claims to have found the answer, there remains a lack of consensus on the initial misunderstanding and the correct approach.

Contextual Notes

Participants are navigating through the definitions and calculations related to vector lengths and dot products, with some expressing confusion over the terminology and methods used. There is also an indication of frustration with the responses received.

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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.
 
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robertjford80 said:
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.

robertjford80 said:
That would be .6 * .8

No.
 
Why not? Saying no, doesn't help me. I already knew it was wrong. And yes I mean dot product.
 
never mind about this. i got the answer now.
 
The dot product of two vectors, <a, b> and <c, d>, is ac+ bd.

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

The length of vector <a, b> is [itex]\sqrt{a^2+ b^2}[/itex].
 

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