Question

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

Answer 1

Step-by-step 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,

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

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