Question

What is `|| < 5 , -6 , 9> + < 2 , -4, -7 > ||`?

Answer 1

`3sqrt(17)`

Explanation:

First, let us calculate the vector sum:

Let `vec(u) \ =<< 5 , -6 , 9>>`
And `vec(v)=<< 2 , -4, -7 >>`

Then:

`vec(u) + vec(v) = << 5 , -6 , 9>> + << 2 , -4, -7 >>`
`" " = << (5)+(2) , (-6)+(-4) , (9)+(-7)>>`
`" " = << 7 , -10 , 2>>`

So then the metric norm is:

`|| vec(u) + vec(v) || = || << 7 , -10 , 2>> ||`
`" " = sqrt((7)^2 + (-10)^2 + (2)^2 )`
`" " = sqrt( 49 + 100 + 4 )`
`" " = sqrt( 153 )`
`" " = 3sqrt(17)`