Question

Calculate the cross product assuming that u × v = <6,2,0>
v*(u + v) =
=

Answer 1

`< -6;-2;0 >`

Explanation:

Let's first remember that

- vector products are distributive;

- cross product is anti-simmetric (ie
`\vec a* \vec b= -\vec b * \vec a`)

- a vector cross multiplied by itself gives the zero vector
`\vec a * \vec a = \vec 0`

We can now solve the equation

`\vec v * (\vec u + \vec v) = (\vec v * \vec u) + (\vec v * \vec v) = - \vec u * \vec v + \vec 0 = < -6; -2; 0 >`