(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In real-number multiplication, ifuv_{1}=uv_{2}andu≠ 0, then we can cancel theuand conclude thatv_{1}=v_{2}. Does the same rule hold for the dot product: Ifu•v_{1}=u•v_{2}andu≠ 0, can you conclude thatv_{1}=v_{2}? Give reasons for your answer.

2. Relevant equations

3. The attempt at a solution

If we letu=k<u_{1}, u_{2}> with u_{2}= 0 and scalark, then the dot product ofuwith any other vectorv=k<v_{1}, v_{2}> will simply be the componentkv_{1}because u_{2}will make theku_{2}kv_{2}product always zero regardless of its value. Thus,vcan be infinitely many different vectors and still have the same dot product withu.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Multi-Variable Calculus: Cancellation of dot products

**Physics Forums | Science Articles, Homework Help, Discussion**