Multiplication using dot product.

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Homework Help Overview

The discussion revolves around the calculation of the dot product of two vectors, A and B, represented in component form. The original poster attempts to find the angle between the vectors using the relationship involving the dot product and the magnitudes of the vectors.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the calculation of the dot product and the subsequent use of trigonometric functions to find the angle. There are questions regarding the correct application of formulas and definitions related to the dot product.

Discussion Status

Participants are actively engaging in checking calculations and definitions related to the dot product. Some guidance has been offered regarding the correct use of trigonometric functions in the context of the problem, with acknowledgment of a misunderstanding in the original approach.

Contextual Notes

There is a noted confusion regarding the use of tangent versus cosine in the calculations, which has led to incorrect results. The participants are working through these definitions and their implications for the problem at hand.

AryRezvani
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Homework Statement



nxtje9.jpg


Homework Equations



Tan θ=A.B/|A|*|B|

The Attempt at a Solution



A=4i-9j
B=9i-6j

A.B=-18
Magnitude of A = √97
Magnitude of B = √117

Solve that out using Cos-1 (-18/Sqr97*Sqr117) and I keep getting the wrong answer.
 
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Check the value you've calculated for A.B :wink:
 
gneill said:
Check the value you've calculated for A.B :wink:

Ahh just caught that. Replugged in the values, and still came out wrong.

Work:

Plugged in 90/(Sqr97*Sqr117) = .8448190756

Tan-1 (.84481...) = 40.191 degrees.

Plugged that into online homework and it was wrong apparently.
 
Check you definition of A.B in terms of magnitudes and angle. You used a correct method in the final line of your first post.
 
gneill said:
Check you definition of A.B in terms of magnitudes and angle. You used a correct method in the final line of your first post.

Could you specify? Are you referring to A.B=|A||B|Cosθ?

Edit: nevermind, got it!
 
AryRezvani said:
Could you specify? Are you referring to A.B=|A||B|Cosθ?

Yup. The formula involves a cosine, so why are you employing ##tan^{-1}##?
 
gneill said:
Yup. The formula involves a cosine, so why are you employing ##tan^{-1}##?

Hahaha thanks, took me a while to catch that.. sadly.
 
AryRezvani said:
Hahaha thanks, took me a while to catch that.. sadly.

Glad I could help :smile:
 

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