Question

Assume that u⋅v=4, ‖u‖=5, and ‖v‖=3. What is the value of 4u⋅(4u−7v)?

Answer 1

Explanation:

It is given that,

`u{\cdot}v=4\\\\|u|=5\\\\|v|=3`

We need to find the value of
`4u{\cdot} (4u-7v)`

Firstly, we should simplify
`4u{\cdot} (4u-7v)`

`4u{\cdot} (4u-7v)=4u{\cdot} 4u-4u{\cdot} 7v`

Now using distributive property : x(y-z)=xy-yz

So,

`4u{\cdot} (4u-7v)=4u{\cdot} 4u-4u{\cdot} 7v\\\\=16u{\cdot}u-28{u{\cdot} v}\\\\=16|u|^2-28(u{\cdot}v)\\\\=16* 5^2-28* 4\\\\=288`

So, the value of
`4u{\cdot} (4u-7v)` is 288.