Chapter 11.3, Problem 63E

To determine

To analyze: and describe the error.

Answer to Problem 63E

The error is $2\left(u\times v\right)=\left(2u\right)\times v=u\times \left(2u\right)\ne 2u\times 2v$

Explanation of Solution

Given information:

The equation is $2\left(u\times v\right)=2u\times 2v\cdots \left(i\right)$

Formula used:

According to the property of cross product

  $k\left(u\times v\right)=\left(ku\right)\times v=u\times \left(ku\right)$

Calculation:

Take the equation in the left hand side of equation $\left(i\right)$

Apply the property discussed above,

  $2\left(u\times v\right)=\left(2u\right)\times v=u\times \left(2u\right)$

Here it can be seen that the above calculation is not equal to the equation present in the right hand side.

Hence there is an error in the give equation and $2\left(u\times v\right)\ne 2u\times 2v.$