(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**

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

# Homework Help: Multi-Variable Calculus: Cancellation of dot products

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